
In this paper, a classical risk model with liquid reserves and proportional investment is considered, and the expected total discounted dividend before ruin of insurance companies under the threshold dividend strategy is studied. First, the integral differential equations of the expected total discounted dividend before ruin satisfying certain boundary conditions is derived. Second, since the explicit solutions of the equations cannot be obtained, the numerical approximation solutions are obtained by the sinc approximation method. Finally, we discuss the effects of parameters such as risk capital ratio and liquid reserve on the expected total discounted dividend before ruin by some examples.
Citation: Chunwei Wang, Shujing Wang, Jiaen Xu, Shaohua Li. Numerical method for a compound Poisson risk model with liquid reserves and proportional investment[J]. AIMS Mathematics, 2024, 9(5): 10893-10910. doi: 10.3934/math.2024532
[1] | Dazhao Chen . Endpoint estimates for multilinear fractional singular integral operators on Herz and Herz type Hardy spaces. AIMS Mathematics, 2021, 6(5): 4989-4999. doi: 10.3934/math.2021293 |
[2] | Anas A. Hijab, Laith K. Shaakir, Sarah Aljohani, Nabil Mlaiki . Double composed metric-like spaces via some fixed point theorems. AIMS Mathematics, 2024, 9(10): 27205-27219. doi: 10.3934/math.20241322 |
[3] | Xianyong Huang, Shanhe Wu, Bicheng Yang . A Hardy-Hilbert-type inequality involving modified weight coefficients and partial sums. AIMS Mathematics, 2022, 7(4): 6294-6310. doi: 10.3934/math.2022350 |
[4] | M. Zakarya, Ghada AlNemer, A. I. Saied, H. M. Rezk . Novel generalized inequalities involving a general Hardy operator with multiple variables and general kernels on time scales. AIMS Mathematics, 2024, 9(8): 21414-21432. doi: 10.3934/math.20241040 |
[5] | Limin Yang, Ruiyun Yang . Some new Hardy-Hilbert-type inequalities with multiparameters. AIMS Mathematics, 2022, 7(1): 840-854. doi: 10.3934/math.2022050 |
[6] | Suriyakamol Thongjob, Kamsing Nonlaopon, Sortiris K. Ntouyas . Some (p, q)-Hardy type inequalities for (p, q)-integrable functions. AIMS Mathematics, 2021, 6(1): 77-89. doi: 10.3934/math.2021006 |
[7] | Chunyan Luo, Yuping Yu, Tingsong Du . Estimates of bounds on the weighted Simpson type inequality and their applications. AIMS Mathematics, 2020, 5(5): 4644-4661. doi: 10.3934/math.2020298 |
[8] | Sabir Hussain, Javairiya Khalid, Yu Ming Chu . Some generalized fractional integral Simpson’s type inequalities with applications. AIMS Mathematics, 2020, 5(6): 5859-5883. doi: 10.3934/math.2020375 |
[9] | Irshad Ayoob, Ng Zhen Chuan, Nabil Mlaiki . Hardy-Rogers type contraction in double controlled metric-like spaces. AIMS Mathematics, 2023, 8(6): 13623-13636. doi: 10.3934/math.2023691 |
[10] | Qing Yang, Chuanzhi Bai . Fixed point theorem for orthogonal contraction of Hardy-Rogers-type mapping on O-complete metric spaces. AIMS Mathematics, 2020, 5(6): 5734-5742. doi: 10.3934/math.2020368 |
In this paper, a classical risk model with liquid reserves and proportional investment is considered, and the expected total discounted dividend before ruin of insurance companies under the threshold dividend strategy is studied. First, the integral differential equations of the expected total discounted dividend before ruin satisfying certain boundary conditions is derived. Second, since the explicit solutions of the equations cannot be obtained, the numerical approximation solutions are obtained by the sinc approximation method. Finally, we discuss the effects of parameters such as risk capital ratio and liquid reserve on the expected total discounted dividend before ruin by some examples.
A multi-attribute decision-making (MADM) tool plays an important role in the environment of fuzzy set theory and to evaluate unreliable and awkward information. According to Yukalov and Sornette [1], it is sometimes very much difficult to handle a huge part of data or information because of either the design of the data or due to the uncertainty involved in the data or information. Human beings have faced such issues for the last few decades. To oversee such issues, Zadeh [2] initiated the notion of fuzzy sets (FS), which takes the truth grade from [0, 1]. Moreover, Atanassove [3] modified the technique of FS and initiated the principle of intuitionistic FS (IFS) by including the falsity grade in FS, with the condition that the sum of both the grades must be less than or equal to 1. Sometimes, when a decision maker provides information, the principle of IFS failed, in which the sum of both the grades exceeds 1. For this situation, Yager [4] introduced the principle of Pythagorean FS (PFS), with the condition that instead of sum of both the grades, the sum of squares of both the grades must not exceed 1. Although with the introduction of PFS, decision makers have gained much more flexibility to give the values of both the grades but yet there can arise many situations, where PFS failed as even the sum of squares of both the grades exceeds 1. To handle this ambiguity, Yager [5] improved the rule of PFS and initiated the notion of q-rung orthopair FS (QROFS), with the rule that the sum of the q-powers (q ≥ 1) of the duplet must not exceeds 1. The QROFS has received massive attraction from many researchers and has utilized in different areas [6,7,8,9,10,11,12,13,14]. The mathematical portrayal of the IFS and their generalizations are clarified with the assistance of Figure 1.
Ramot et al. [15] investigated the idea of complex FS (CFS) by including the unreal part in the truth grade, called complex truth grade, whose real and unreal parts belong to [0, 1]. Due to certain complications, Alkouri and Salleh [16] modified the principle of CFS by including the falsity grade in the CFS to elaborate the complex IFS (CIFS), with the rule that the sum of the real and unreal parts of the duplet must be limited to [0, 1]. Moreover, Ullah [17] utilized the idea of complex PFS (CPFS) by improving the rule of IFS to initiate a new rule for CPFS, with the condition that the sum of the squares of the real and unreal parts of the duplet must be limited to [0, 1]. Akram and Naz initiated decision making for CPFS [18]. Although CPFS has proved its effectiveness, there are many situations where it fails to perform, for instance, when a decision maker provides such sorts of information whose sum of the squares of the real and unreal parts exceeds from [0, 1]; for this, the complex QROFS (CQROFS) was developed by Liu et al. [19,20]. Furthermore, the CQROFS is portrayed by the interest degree and the non-participation degree, who's total q-powers of the genuine part (likewise for nonexistent part) are not by and large or comparable to 1. The CQROFS is much more generalized and helpful to the researchers of the field as compared to CPFS and CIFS. Mahmood and Ali [21,22] enhanced the effectiveness of the notion of CQROFS by studying the TOPSIS technique, correlation coefficients, and Maclaurin operators in the environment of CQROFS.
In terms of the real-life importance of linguistic terms (LT), Zadeh [23] introduced the theory of LT sets (LTS) for evaluating the awkward and unreliable problems in real-life decisions. Furthermore, Herrera and Martinez [24] pioneered the theory of the 2-tuple LT (2TLT) set, which is more modified than the LTSs. Herrera and Martinez [25,26] utilized the theory of LTS in different fields. Li and Liu [27] initiated the theory of Heronian mean operators for 2TLT.
DTRS is one of the capable methods to assess abnormal and convoluted data. Different researchers have adjusted it to various ways like loss function (LF) [28], trait decrease [29], and further developed models utilizing DTRS [30]. Yao [31] introduced the three-ways decision (3WD), which is changed from DTRS to adapt to practical choice issues. 3WD can isolate all widespread sets into three distinct parts: the positive area (POS(C)), the negative district (NEG(C)), and the limit locale (BND(C)). As a mix of DTRSs and the Bayesian choice method, the procedures of 3WD has successfully overseen numerous request issues. This speculation has been applied in various fields [32,33]. The graphical portrayal of the 3WD dependent on the harsh set is examined with the assistance of Figure 2.
Liu and Yang [34] introduced the misfortune work in 3WDs dependent on intuitionistic fuzzy linguistic sets. In view of the above examination, we initiated the following: we generalize the massive important techniques of three-way decisions (3WD) [35] and DTRS with Complex q-rung orthopair 2-tuple linguistic variable (CQRO2-TLV), to elaborate certain important properties. Moreover, the generalized Maclurin symmetric mean (GMSM) [36] is a dominant and more flexible method to determine the accuracy and dominancy of real life issues. Therefore, by considering the complex q-rung orthopair 2-tuple linguistic (CQRO2-TL) information and generalized Maclurin symmetric mean (GMSM), we present the CQRO2-TL GMSM (CQRO2-TLGMSM) operator and weighted CQRO2-TL GMSM (WCQRO2-TLGMSM) operator, and demonstrated their effective properties. Finally, a model is applied to exhaustively elucidate the proposed procedure, and the effects of different contingent probabilities on choice results are examined. The investigation of the elaborated approach is likewise discussed regarding certain ways to deal with the capability and capacity of the presented approach. For simplicity, the explored work for this manuscript is explained with the help of Figure 3.
This manuscript is outlined as follows. In Section 2, we briefly audit some helpful ideas of 2-TLF [24], converse 2-TLF [24], CQROFS [19,20,21,22,35], and their functional laws. Furthermore, the GMSM operators [36] are discussed. In Section 3, we explored CQRO2-TLV and their algebraic laws. In Section 4, we generalize 3WD and DTRS with CQRO2-TLV to elaborate certain important properties. GMSM is a dominant and more flexible way to determine the accuracy and dominancy of real life issues. Therefore, by considering the CQRO2-TL information and GMSM, in section 5 we present the CQRO2-TLGMSM operator and the WCQRO2-TLGMSM operator and demonstrated their effective properties. In Section 6, a model is applied to exhaustively elucidate the proposed procedure, and the effects of different contingent probabilities on choice results are examined. The conclusion of this manuscript is discussed in Section 7.
For the convenience and improved understanding for the reader, in this section we will recall some basic notions which will be used in the manuscript. The symbols ỮUNI,μQCQ(ử), and ηQCQ(ử) will denote the universal set, the truth grade, and the falsity grade, respectively, where αSC,δSC,qSC≥1.
Definition 2.1. [24] For a LS SLT={sSLT−0,sSLT−1,sSLT−2,sSLT−3,….,sSLT−g} with βSC∈[0,1], the 2-TL function ΔLT is given by:
ΔLT:[0,1]→SLT×[−12g,12g}, | (2.1) |
ΔLT(βSC)=(sSLT−j,αSC)with{sSLT−jj=round(βSC,g)αSC=βSC−jgαSC∈[−12g,12g}. | (2.2) |
The 2-TL inverse function Δ−1LT is given by:
Δ−1LT:SLT×[−12g,12g}→[0,1], | (2.3) |
Δ−1LT(sSLT−j,αSC)=jg+αSC=βSC. | (2.4) |
Definition 2.2. [19] A CQROFS is given by
QCQ={(μQCQ(ử),ηQCQ(ử)):ử∈ỮUNI} | (2.5) |
where μQCQ(ử)=μQCQRP(ử)ei2π(μQCQIP(ử)) and ηQCQ(ử)=ηQCQRP(ử)ei2π(ηQCQIP(ử)),
with the conditions: 0≤μqSCQCQRP(ử)+ηqSCQCQRP(ử)≤1,0≤μqSCQCQIP(ử)+ηqSCQCQIP(ử)≤1.
Moreover, ζQCQ(ử)=(1−(μqSCQCQRP(ử)+ηqSCQCQRP(ử))1qSC)ei2π(1−(μqSCQCQIP(ử)+ηqSCQCQIP(ử))1qSC) is called the refusal grade. The QROFN is given as
QCQ=(μQCQ,ηQCQ)=(μQCQRPei2π(μQCQIP),ηQCQRPei2π(ηQCQIP)). |
Definition 2.3. [20] For any two CQROFNs
QCQ−1=(μQCQRP−1ei2π(μQCQIP−1),ηQCQRP−1ei2π(ηQCQIP−1)) and
QCQ−2=(μQCQRP−2ei2π(μQCQIP−2),ηQCQRP−2ei2π(ηQCQIP−2)), then
(1). QCQ−1⊕CQQCQ−2=((μqCQQCQRP−1+μqCQQCQRP−2−μqCQQCQRP−1μqCQQCQRP−2)1qCQei2π(μqCQQCQIP−1+μqCQQCQIP−2−μqCQQCQIP−1μqCQQCQIP−2)1qCQ,ηQCQRP−1ηQCQRP−2ei2π(ηQCQIP−1ηQCQIP−2));
(2). QCQ−1⊗CQQCQ−2=(μQCQRP−1μQCQRP−2ei2π(μQCQIP−1μQCQIP−2),(ηqCQQCQRP−1+ηqCQQCQRP−2−ηqCQQCQRP−1ηqCQQCQRP−2)1qCQei2π(ηqCQQCQIP−1+ηqCQQCQIP−2−ηqCQQCQIP−1ηqCQQCQIP−2)1qCQ);
(3). QδSCCQ−1=(μδSCQCQRP−1ei2π(μδSCQCQIP−1),(1−(1−ηqCQQCQRP−1)δSC)1qCQei2π(1−(1−ηqCQQCQIP−1)δSC)1qCQ);
(4). δSCQCQ−1=((1−(1−μqCQQCQRP−1)δSC)1qCQei2π(1−(1−μqCQQCQIP−1)δSC)1qCQ,ηδSCQCQRP−1ei2π(ηδSCQCQIP−1)).
Definition 2.4. [21] For any two CQROFNs
QCQ−1=(μQCQRP−1ei2π(μQCQIP−1),ηQCQRP−1ei2π(ηQCQIP−1)) and
QCQ−2=(μQCQRP−2ei2π(μQCQIP−2),ηQCQRP−2ei2π(ηQCQIP−2)), the score and accuracy functions are given by:
Ş(QCQ−1)=(μqSCQCQRP−1−ηqSCQCQRP−1+μqSCQCQIP−1−ηqSCQCQIP−1)2, | (2.6) |
Ȟ(QCQ−1)=(μqSCQCQRP−1+ηqSCQCQRP−1+μqSCQCQIP−1+ηqSCQCQIP−1)2. | (2.7) |
Based on the two above notions, the compassion between two CQROFNs is given by:
(1). If Ş(QCQ−1)>Ş(QCQ−2), then QCQ−1>QCQ−2;
(2). If Ş(QCQ−1)=Ş(QCQ−2), then:
ⅰ) if Ȟ(QCQ−1)>Ȟ(QCQ−2), then QCQ−1>QCQ−2;
ⅱ) if Ȟ(QCQ−1)=Ȟ(QCQ−2), then QCQ−1=QCQ−2.
Definition 2.5. [36] For the family of QCQ−j(j=1,2,3,…,n), the MSM operator is given by:
MSMKSC(QCQ−1,QCQ−2,…,QCQ−n)=(∑1≤j1≤⋯≤jKSC∏KSCi=1QCQ−jiCKSCn)1KSC | (2.8) |
where KSC=1,2,…,n,(j1,j2,…,jKSC) denotes the K-tuple kind of (1,2,..,n), and the symbol CKSCn designates the binomial co-efficient (BCO). Furthermore:
(1). MSMKSC(QCQ,QCQ,…,QCQ)=QCQ;
(2). MSMKSC(QCQ−1,QCQ−2,…,QCQ−n)≤MSMKSC(QCQ−∗1,QCQ−∗2,…,QCQ−∗n), if QCQ−j≤QCQ−∗j for all j.
(3). minjQCQ−j≤MSMKSC(QCQ−1,QCQ−2,…,QCQ−n)≤maxjQCQ−j.
Definition 2.6. [36] For the family of QCQ−j(j=1,2,3,…,n), the GMSM operator is given by:
GMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(QCQ−1,QCQ−2,…,QCQ−n)=(∑1≤j1≤⋯≤jKSC∏KSCi=1QαSC−iCQ−jiCKSCn)1αSC−1+αSC−2+⋯+αSC−KSC | (2.9) |
where KSC=1,2,…,n,αSC−1,αSC−2,…,αSC−KSC≥0,(j1,j2,…,jKSC) signifies the K-tuple collection of (1,2,..,n). Furthermore:
(1). GMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(QCQ,QCQ,…,QCQ) =QCQ,GMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(0,0,…,0)=0;
(2). GMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(QCQ−1,QCQ−2,…,QCQ−n)≤ GMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(QCQ−∗1,QCQ−∗2,…,QCQ−∗n), if QCQ−j≤QCQ−∗j for all j;
(3). minjQCQ−j≤GMSM(KSC,αSC−1,αSC−2,…,αSC−KSC) (QCQ−1,QCQ−2,…,QCQ−n)≤maxjQCQ−j.
As discussed in [34], DTRS contains two status and three actions, whose information: ΩS={FB,∼FNB} and AAC={χPAC,χBAC,χNAC}, where ΩS is utilized for having a place and for to be not having a place and AAC is utilized for +ve, limit and -ve. Table 1 shows the lose capacities and their portrayals.
Symbols | FB(PAC)=Correctlysolved | ∼FNB(NAC)=wronglysolved |
χPAC | −QCQ−PACPAC | −QCQ−PACNAC |
χBAC | −QCQ−BACPAC | −QCQ−BACNAC |
χNAC | −QCQ−NACPAC | −QCQ−NACNAC |
Note: −QCQ−PACPAC,−QCQ−PACNAC= Expenses of right sort and mistake sort of idea ử in agreed judgment; −QCQ−BACPAC,−QCQ−BACNAC=Expensesoftherightsortandmistakesortoftheideaửinabstinacejudgment;−QCQ−NACPAC,−QCQ−NACNAC= Expensesoftherightsortandmistakesortoftheideaửinnon−agreedjudgment. |
Form Table 1, the inequality is given as follows:
−QCQ−PACPAC<−QCQ−BACPAC<−QCQ−NACPAC, | (2.10) |
−QCQ−NACNAC<−QCQ−BACNAC<−QCQ−PACNAC. | (2.11) |
Given the Bayesian risk choice hypothesis [34], we have:
Pr(FB|[ử])+Pr(∼FNB|[ử])=1. | (2.12) |
By using the Eq (2.12), the expected losses YEL(χjAC|[ử]),j=P,B,N, and the different actions are expressed below:
YEL(χPAC|[ử])=−QCQ−PACPACPr(FB|[ử])+−QCQ−PACNACPr(∼FNB|[ử]), | (2.13) |
YEL(χBAC|[ử])=−QCQ−BACPACPr(FB|[ử])+−QCQ−BACNACPr(∼FNB|[ử]), | (2.14) |
YEL(χNAC|[ử])=−QCQ−NACPACPr(FB|[ử])+−QCQ−NACNACPr(∼FNB|[ử]). | (2.15) |
From the above information, we have:
PAC:WhenYEL(χPAC|[ử])≤YEL(χBAC|[ử])andYEL(χPAC|[ử])≤YEL(χNAC|[ử]),thenử∈POS(FP); | (2.16) |
BAC:WhenYEL(χBAC|[ử])≤YEL(χPAC|[ử])andYEL(χBAC|[ử])≤YEL(χNAC|[ử]),thenử∈BUN(FB); | (2.17) |
NAC:WhenYEL(χNAC|[ử])≤YEL(χPAC|[ử])andYEL(χNAC|[ử])≤YEL(χBAC|[ử]),thenử∈NRG(FN). | (2.18) |
Based on the above analysis, we have explored the novel approach of CQRO2-TLS and its fundamental properties. These properties are also explained with the help of some numerical examples.
Definition 3.1. A CQRO2-TLS is given by
QCQTL={((sSLT(ử),αSC),(μQCQTL(ử),ηQCQTL(ử))):ử∈ỮUNI} | (3.1) |
where μQCQTL(ử)=μQCQTLRP(ử)ei2π(μQCQTLIP(ử)) and ηQCQTL(ử)=ηQCQTLRP(ử)ei2π(ηQCQTLIP(ử)), with the conditions: 0≤μqSCQCQTLRP(ử)+ηqSCQCQTLRP(ử)≤1,0≤μqSCQCQTLIP(ử)+ηqSCQCQTLIP(ử)≤1, where qSC expresses the rational numbers and the pair (sSLT(ử),αSC) is called 2-TLV with αSC∈[−12g,12g} and sSLT(ử)∈SLT.
Moreover,
ζQCQTL(ử)=(1−(μqSCQCQTLRP(ử)+ηqSCQCQTLRP(ử))1qSC)ei2π(1−(μqSCQCQTLIP(ử)+ηqSCQCQTLIP(ử))1qSC) is called the refusal grade. The CQRO2T-LN is shown by:
QCQTL=((sSLT,αSC),(μQCQTL,ηQCQTL))=((sSLT,αSC),(μQCQTLRPei2π(μQCQTLIP),ηQCQTLRPei2π(ηQCQTLIP))). |
Definition 3.2. For any two CQRO2-TLNs
QCQTL−1=((sSLT−1,αSC−1),(μQCQTLRP−1ei2π(μQCQTLIP−1),ηQCQTLRP−1ei2π(ηQCQTLIP−1))) and QCQTL−2=((sSLT−2,αSC−2),(μQCQTLRP−2ei2π(μQCQTLIP−2),ηQCQTLRP−2ei2π(ηQCQTLIP−2))),
(1). QCQTL−1⊕CQTLQCQTL−2=(ΔLT(Δ−1LT(sSLT−1,αSC−1)+Δ−1LT(sSLT−2,αSC−2)).((μqCQQCQTLRP−1+μqCQQCQTLRP−2−μqCQQCQTLRP−1μqCQQCQTLRP−2)1qCQei2π(μqCQQCQTLIP−1+μqCQQCQTLIP−2−μqCQQCQTLIP−1μqCQQCQTLIP−2)1qCQ,ηQCQTLRP−1ηQCQTLRP−2ei2π(ηQCQTLIP−1ηQCQTLIP−2)));
(2). QCQTL−1⊗CQTLQCQTL−2=(ΔLT(Δ−1LT(sSLT−1,αSC−1)×Δ−1LT(sSLT−2,αSC−2)).(μQCQTLRP−1μQCQTLRP−2ei2π(μQCQTLIP−1μQCQTLIP−2),(ηqCQQCQTLRP−1+ηqCQQCQTLRP−2−ηqCQQCQTLRP−1ηqCQQCQTLRP−2)1qCQei2π(ηqCQQCQTLIP−1+ηqCQQCQTLIP−2−ηqCQQCQTLIP−1ηqCQQCQTLIP−2)1qCQ));
(3). QδSCCQTL−1=(ΔLT(Δ−1LT(sSLT−1,αSC−1)δSC),μδSCQCQTLRP−1ei2π(μδSCQCQTLIP−1),((1−(1−ηqCQQCQTLRP−1)δSC)1qCQei2π(1−(1−ηqCQQCQTLIP−1)δSC)1qCQ));
(4). δSCQCQTL−1=(ΔLT(δSC×Δ−1LT(sSLT−1,αSC−1)),((1−(1−μqCQQCQTLRP−1(ử))δSC)1qCQei2π(1−(1−μqCQQCQTLIP−1(ử))δSC)1qCQ,ηδSCQCQTLRP−1ei2π(ηδSCQCQTLIP−1))).
Definition 3.3. For any two QROF2-TLNs
QCQTL−1=((sSLT−1,αSC−1),(μQCQTLRP−1ei2π(μQCQTLIP−1),ηQCQTLRP−1ei2π(ηQCQTLIP−1))) and QCQTL−2=((sSLT−2,αSC−2),(μQCQTLRP−2ei2π(μQCQTLIP−2),ηQCQTLRP−2ei2π(ηQCQTLIP−2))), the score and accuracy functions are given by:
Ş(QCQTL−1)=Δ−1LT(sSLT−1,αSC−1)×(1+μqSCQCQTLRP−1+μqSCQCQTLIP−1−ηqSCQCQTLRP−1−ηqSCQCQTLIP−1)2, | (3.2) |
Ȟ(QCQTL−1)=Δ−1LT(sSLT−1,αSC−1)×(μqSCQCQTLRP−1+μqSCQCQTLIP−1+ηqSCQCQTLRP−1+ηqSCQCQTLIP−1). | (3.3) |
Based on the two above notions, the compassion between two QROF2-TLNs is given by:
(1). If Ş(QCQTL−1)>Ş(QCQTL−2), then QCQTL−1>QCQTL−2;
(2). If Ş(QCQTL−1)=Ş(QCQTL−2), then:
ⅰ) Ȟ(QCQTL−1)>Ȟ(QCQTL−2), implies QCQTL−1>QCQTL−2;
ⅱ) Ȟ(QCQTL−1)=Ȟ(QCQTL−2), implies QCQTL−1=QCQTL−2.
Symbols | FB(PAC)=Correctlysolved | ∼FNB(NAC)=wronglysolved |
χPAC | QCQTL−−QCQ−PACPAC=((sSLT(−QCQ−PACPAC),αSC),(μQCQTLRP(−QCQ−PACPAC)ei2π(μQCQTLIP(−QCQ−PACPAC)),ηQCQTLRP(−QCQ−PACPAC)ei2π(ηQCQTLIP(−QCQ−PACPAC)))) | QCQTL−−QCQ−NACPAC=((sSLT(−QCQ−NACPAC),αSC),(μQCQTLRP(−QCQ−NACPAC)ei2π(μQCQTLIP(−QCQ−NACPAC)),ηQCQTLRP(−QCQ−NACPAC)ei2π(ηQCQTLIP(−QCQ−NACPAC)))) |
χBAC | QCQTL−−QCQ−BACPAC=((sSLT(−QCQ−BACPAC),αSC),(μQCQTLRP(−QCQ−BACPAC)ei2π(μQCQTLIP(−QCQ−BACPAC)),ηQCQTLRP(−QCQ−BACPAC)ei2π(ηQCQTLIP(−QCQ−BACPAC)))) | QCQTL−−QCQ−BACNAC=((sSLT(−QCQ−BACNAC),αSC),(μQCQTLRP(−QCQ−BACNAC)ei2π(μQCQTLIP(−QCQ−BACNAC)),ηQCQTLRP(−QCQ−BACNAC)ei2π(ηQCQTLIP(−QCQ−BACNAC)))) |
χNAC | QCQTL−−QCQ−NACPAC=((sSLT(−QCQ−NACPAC),αSC),(μQCQTLRP(−QCQ−NACPAC)ei2π(μQCQTLIP(−QCQ−NACPAC)),ηQCQTLRP(−QCQ−NACPAC)ei2π(ηQCQTLIP(−QCQ−NACPAC)))) | QCQTL−−QCQ−NACPAC=((sSLT(−QCQ−NACNAC),αSC),(μQCQTLRP(−QCQ−NACNAC)ei2π(μQCQTLIP(−QCQ−NACNAC)),ηQCQTLRP(−QCQ−NACNAC)ei2π(ηQCQTLIP(−QCQ−NACNAC)))) |
Note: QCQTL−−QCQ−PACPAC,QCQTL−−QCQ−PACNAC= Expensesoftherightsortand mistakesortof theideaửinagreedjudgment; QCQTL−−QCQ−BACPAC,QCQTL−−QCQ−BACNAC=Expensesofthe rightsortandmistakesortoftheideaửin abstinancejudgment;QCQTL−−QCQ−NACPAC,QCQTL−−QCQ−NACNAC= Expensesoftherightsortandmistake sortoftheideaửinnon−agreedjudgment. |
The purpose of this section is to explore the novel DTRS model by using the CQROF2-TLV based on three-way decisions. The LF matrix for CQROF2-TLV is presented in Table 2.
Form Table 2, the inequality is given as:
QCQTL−−QCQ−PACPAC<QCQTL−−QCQ−BACPAC<QCQTL−−QCQ−NACPAC, | (4.1) |
QCQTL−−QCQ−NACNAC<QCQTL−−QCQ−BACNAC<QCQTL−−QCQ−PACNAC. | (4.2) |
Furthermore, by using the Eq (4.2), we explain the expected losses YEL(χjAC|[ử]),j=P,B,N and the different actions are expressed below:
YEL(χPAC|[ử])=QCQTL−−QCQ−PACPACPr(FB|[ử])⊕CQTLQCQTL−−QCQ−PACPACPr(∼FNB|[ử]), | (4.3) |
YEL(χBAC|[ử])=QCQTL−−QCQ−BACPACPr(FB|[ử])⊕CQTLQCQTL−−QCQ−BACNACPr(∼FNB|[ử]), | (4.4) |
YEL(χNAC|[ử])=QCQTL−−QCQ−NACPACPr(FB|[ử])⊕CQTLQCQTL−−QCQ−NACNACPr(∼FNB|[ử]). | (4.5) |
Assumed that Pr(FB|[ử])=δB and Pr(∼FNB|[ử])=δNB, then the Eq (4.2) is given as: δB+δNB=1.
Theorem 4.1. With usual meanings
YEL(χPAC|[ử])=(ΔLT(δB×Δ−1LT(sSLT(−QCQ−PACPAC),αSC)+δNB×Δ−1LT(sSLT(−QCQ−PACNAC),αSC)),((1−(1−μqCQQCQTLRP(−QCQ−PACPAC))δB(1−μqCQQCQTLRP(−QCQ−PACNAC))δNB)1qCQ×ei2π(1−(1−μqCQQCQTLIP(−QCQ−PACPAC))δB(1−μqCQQCQTLIP(−QCQ−PACNAC))δNB)1qCQ,((ηQCQTLRP(−QCQ−PACPAC))δB×(ηQCQTLRP(−QCQ−PACNAC))δNB)ei2π((ηQCQTLIP(−QCQ−PACPAC))δB×(ηQCQTLIP(−QCQ−PACNAC))δNB))), | (4.6) |
YEL(χBAC|[ử])=(ΔLT(δB×Δ−1LT(sSLT(−QCQ−BACPAC),αSC)+δNB×Δ−1LT(sSLT(−QCQ−BACNAC),αSC)),((1−(1−μqCQQCQTLRP(−QCQ−BACPAC))δB(1−μqCQQCQTLRP(−QCQ−BACNAC))δNB)1qCQ×ei2π(1−(1−μqCQQCQTLIP(−QCQ−BACPAC))δB(1−μqCQQCQTLIP(−QCQ−BACNAC))δNB)1qCQ,((ηQCQTLRP(−QCQ−BACPAC))δB×(ηQCQTLRP(−QCQ−BACNAC))δNB)ei2π((ηQCQTLIP(−QCQ−BACPAC))δB×(ηQCQTLIP(−QCQ−BACNAC))δNB))), | (4.7) |
YEL(χNAC|[ử])=(ΔLT(δB×Δ−1LT(sSLT(−QCQ−NACPAC),αSC)+δNB×Δ−1LT(sSLT(−QCQ−NACNAC),αSC)),((1−(1−μqCQQCQTLRP(−QCQ−NACPAC))δB(1−μqCQQCQTLRP(−QCQ−NACNAC))δNB)1qCQ×ei2π(1−(1−μqCQQCQTLIP(−QCQ−NACPAC))δB(1−μqCQQCQTLIP(−QCQ−NACNAC))δNB)1qCQ,((ηQCQTLRP(−QCQ−NACPAC))δB×(ηQCQTLRP(−QCQ−NACNAC))δNB)ei2π((ηQCQTLIP(−QCQ−NACPAC))δB×(ηQCQTLIP(−QCQ−NACNAC))δNB))). | (4.8) |
Proof. First, we prove that the Eq (4.6) holds. The proofs of Eq (4.7) and of Eq (4.8) are similar.
YEL(χPAC|[ử])=QCQTL−−QCQ−PACPACPr(FB|[ử])⊕CQTLQCQTL−−QCQ−PACPACPr(∼FNB|[ử])=QCQTL−−QCQ−PACPACδB⊕CQTLQCQTL−−QCQ−PACPACδNB=((ΔLT(δB×Δ−1LT(sSLT(−QCQ−PACPAC),αSC)),((1−(1−μqCQQCQTLRP(−QCQ−PACPAC))δB)1qCQei2π(1−(1−μqCQQCQTLIP(−QCQ−PACPAC))δB)1qCQ,(ηQCQTLRP(−QCQ−PACPAC))δBei2π(ηQCQTLIP(−QCQ−PACPAC))δB))⊕CQTL(ΔLT(δNB×Δ−1LT(sSLT(−QCQ−PACNAC),αSC)),((1−(1−μqCQQCQTLRP(−QCQ−PACNAC))δB)1qCQei2π(1−(1−μqCQQCQTLIP(−QCQ−PACNAC))δB)1qCQ,(ηQCQTLRP(−QCQ−PACNAC))δBei2π(ηQCQTLIP(−QCQ−PACNAC))δB)))=(ΔLT(δB×Δ−1LT(sSLT(−QCQ−PACPAC),αSC)+δNB×Δ−1LT(sSLT(−QCQ−PACNAC),αSC)),((1−(1−μqCQQCQTLRP(−QCQ−PACPAC))δB(1−μqCQQCQTLRP(−QCQ−PACNAC))δNB)1qCQ×ei2π(1−(1−μqCQQCQTLIP(−QCQ−PACPAC))δB(1−μqCQQCQTLIP(−QCQ−PACNAC))δNB)1qCQ,((ηQCQTLRP(−QCQ−PACPAC))δB×(ηQCQTLRP(−QCQ−PACNAC))δNB)ei2π((ηQCQTLIP(−QCQ−PACPAC))δB×(ηQCQTLIP(−QCQ−PACNAC))δNB))) |
Moreover, we diagnose the expected values, such that
QEV(YEL(χPAC|[ử]))=((δB×Δ−1LT(sSLT(−QCQ−PACPAC),αSC)+δNB×Δ−1LT(sSLT(−QCQ−PACNAC),αSC))×((1−(1−μqCQQCQTLRP(−QCQ−PACPAC))δB(1−μqCQQCQTLRP(−QCQ−PACNAC))δNB)1qCQ+(1−(1−μqCQQCQTLIP(−QCQ−PACPAC))δB(1−μqCQQCQTLIP(−QCQ−PACNAC))δNB)1qCQ−(ηQCQTLRP(−QCQ−PACPAC))δB(ηQCQTLRP(−QCQ−PACNAC))δNB−(ηQCQTLRP(−QCQ−PACPAC))δB(ηQCQTLRP(−QCQ−PACNAC))δNB))8, | (4.9) |
QEV(YEL(χBAC|[ử]))=((δB×Δ−1LT(sSLT(−QCQ−BACPAC),αSC)+δNB×Δ−1LT(sSLT(−QCQ−BACNAC),αSC))×((1−(1−μqCQQCQTLRP(−QCQ−BACPAC))δB(1−μqCQQCQTLRP(−QCQ−BACNAC))δNB)1qCQ+(1−(1−μqCQQCQTLIP(−QCQ−BACPAC))δB(1−μqCQQCQTLIP(−QCQ−BACNAC))δNB)1qCQ−(ηQCQTLRP(−QCQ−BACPAC))δB(ηQCQTLRP(−QCQ−BACNAC))δNB−(ηQCQTLRP(−QCQ−BACPAC))δB(ηQCQTLRP(−QCQ−BACNAC))δNB))8, | (4.10) |
QEV(YEL(χDAC|[ử]))=((δB×Δ−1LT(sSLT(−QCQ−NACPAC),αSC)+δNB×Δ−1LT(sSLT(−QCQ−NACNAC),αSC))×((1−(1−μqCQQCQTLRP(−QCQ−NACPAC))δB(1−μqCQQCQTLRP(−QCQ−NACNAC))δNB)1qCQ+(1−(1−μqCQQCQTLIP(−QCQ−NACPAC))δB(1−μqCQQCQTLIP(−QCQ−NACNAC))δNB)1qCQ−(ηQCQTLRP(−QCQ−NACPAC))δB(ηQCQTLRP(−QCQ−NACNAC))δNB−(ηQCQTLRP(−QCQ−NACPAC))δB(ηQCQTLRP(−QCQ−NACNAC))δNB))8. | (4.11) |
To handle whenever the normal qualities failed to discover the connections between any of two predictable losses, we investigate the ideas of precision work, which is expressed as follows:
GAF(YEL(χPAC|[ử]))=((δB×Δ−1LT(sSLT(−QCQ−PACPAC),αSC)+δNB×Δ−1LT(sSLT(−QCQ−PACNAC),αSC))×((1−(1−μqCQQCQTLRP(−QCQ−PACPAC))δB(1−μqCQQCQTLRP(−QCQ−PACNAC))δNB)1qCQ+(1−(1−μqCQQCQTLIP(−QCQ−PACPAC))δB(1−μqCQQCQTLIP(−QCQ−PACNAC))δNB)1qCQ+(ηQCQTLRP(−QCQ−PACPAC))δB(ηQCQTLRP(−QCQ−PACNAC))δNB+(ηQCQTLRP(−QCQ−PACPAC))δB(ηQCQTLRP(−QCQ−PACNAC))δNB))8, | (4.12) |
GAF(YEL(χBAC|[ử]))=((δB×Δ−1LT(sSLT(−QCQ−BACPAC),αSC)+δNB×Δ−1LT(sSLT(−QCQ−BACNAC),αSC))×((1−(1−μqCQQCQTLRP(−QCQ−BACPAC))δB(1−μqCQQCQTLRP(−QCQ−BACNAC))δNB)1qCQ+(1−(1−μqCQQCQTLIP(−QCQ−BACPAC))δB(1−μqCQQCQTLIP(−QCQ−BACNAC))δNB)1qCQ+(ηQCQTLRP(−QCQ−BACPAC))δB(ηQCQTLRP(−QCQ−BACNAC))δNB+(ηQCQTLRP(−QCQ−BACPAC))δB(ηQCQTLRP(−QCQ−BACNAC))δNB))8, | (4.13) |
GAF(YEL(χDAC|[ử]))=((δB×Δ−1LT(sSLT(−QCQ−NACPAC),αSC)+δNB×Δ−1LT(sSLT(−QCQ−NACNAC),αSC))×((1−(1−μqCQQCQTLRP(−QCQ−NACPAC))δB(1−μqCQQCQTLRP(−QCQ−NACNAC))δNB)1qCQ+(1−(1−μqCQQCQTLIP(−QCQ−NACPAC))δB(1−μqCQQCQTLIP(−QCQ−NACNAC))δNB)1qCQ+(ηQCQTLRP(−QCQ−NACPAC))δB(ηQCQTLRP(−QCQ−NACNAC))δNB+(ηQCQTLRP(−QCQ−NACPAC))δB(ηQCQTLRP(−QCQ−NACNAC))δNB))8. | (4.14) |
Furthermore, we diagnosed the three-way decision rules, such that
PAC−1:WhenQEV(YEL(χPAC|[ử]))<QEV(YEL(χBAC|[ử]))∨QEV(YEL(χPAC|[ử]))=QEV(YEL(χBAC|[ử]))∧GAF(YEL(χPAC|[ử]))≤GAF(YEL(χBAC|[ử]))∧QEV(YEL(χPAC|[ử]))<QEV(YEL(χNAC|[ử]))∨QEV(YEL(χPAC|[ử]))=QEV(YEL(χNAC|[ử]))∧GAF(YEL(χPAC|[ử]))≤GAF(YEL(χNAC|[ử])),thenử∈POS(FP); | (4.15) |
BAC−1:WhenQEV(YEL(χBAC|[ử]))<QEV(YEL(χPAC|[ử]))∨QEV(YEL(χBAC|[ử]))=QEV(YEL(χPAC|[ử]))∧GAF(YEL(χBAC|[ử]))≤GAF(YEL(χPAC|[ử]))∧QEV(YEL(χBAC|[ử]))<QEV(YEL(χNAC|[ử]))∨QEV(YEL(χBAC|[ử]))=QEV(YEL(χNAC|[ử]))∧GAF(YEL(χBAC|[ử]))≤GAF(YEL(χNAC|[ử])),thenử∈BUN(FP); | (4.16) |
NAC−1:WhenQEV(YEL(χNAC|[ử]))<QEV(YEL(χPAC|[ử]))∨QEV(YEL(χNAC|[ử]))=QEV(YEL(χPAC|[ử]))∧GAF(YEL(χNAC|[ử]))≤GAF(YEL(χPAC|[ử]))∧QEV(YEL(χNAC|[ử]))<QEV(YEL(χBAC|[ử]))∨QEV(YEL(χNAC|[ử]))=QEV(YEL(χBAC|[ử]))∧GAF(YEL(χNAC|[ử]))≤GAF(YEL(χBAC|[ử])),thenử∈NEG(FP). | (4.17) |
Therefore,
GAF(QCQTL−−QCQ−PACPAC)<GAF(QCQTL−−QCQ−BACPAC)<GAF(QCQTL−−QCQ−NACPAC), | (4.18) |
GAF(QCQTL−−QCQ−NACNAC)<GAF(QCQTL−−QCQ−BACNAC)<GAF(QCQTL−−QCQ−PACNAC). | (4.19) |
The interrelationship among the different attributes in real decision theory is ever-present. The MSM and GMSM operators are efficient techniques to perfectly evaluate the interrelation between the characteristics. The purpose of this communication is to explore the GMSM and weighted GMSM based on CQRO2-TLVs.
Definition 5.1. For the family of CQRO2-TLVs QCQTL−j(j=1,2,3,…,n), the CQRO2-TLGMSM operator is given by:
CQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(QCQTL−1,QCQTL−2,…,QCQTL−n)=(∑1≤j1≤⋯≤jKSC∏KSCi=1QαSC−iCQTL−jiCKSCn)1αSC−1+αSC−2+⋯+αSC−KSC | (5.1) |
where KSC=1,2,…,n,αSC−1,αSC−2,…,αSC−KSC≥0,(j1,j2,…,jKSC) designates the K-tuple collection of (1,2,..,n).
Theorem 5.2. For the family of CQRO2-TLVs
QCQTL−j=((sSLT−j,αSC−j),(μQCQTLRP−jei2π(μQCQTLIP−j),ηQCQTLRP−jei2π(ηQCQTLIP−j)))(j=1,2,3,…,n),
CQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(QCQTL−1,QCQTL−2,…,QCQTL−n)=(ΔLT((∑1≤j1≤⋯≤jKSC∏KSCi=1(Δ−1LT(sSLT−ji,αSC−ji))αSC−iCKSCn)1αSC−1+αSC−2+⋯+αSC−KSC),(((1−∏1≤j1≤⋯≤jKSC(1−KSC∏i=1(μqCQQCQTLRP−j)αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQ×ei2π(((1−∏1≤j1≤⋯≤jKSC(1−∏KSCi=1(μqCQQCQTLIP−j)αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQ),(1−(1−∏1≤j1≤⋯≤jKSC(1−KSC∏i=1(1−ηqCQQCQTLRP−j)αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQ×ei2π(1−(1−∏1≤j1≤⋯≤jKSC(1−∏KSCi=1(1−ηqCQQCQTLIP−j)αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQ)). | (5.2) |
Proof. Let
KSC∏i=1QαSC−iCQTL−ji=(ΔLT(KSC∏i=1(Δ−1LT(sSLT−ji,αSC−ji))αSC−i),(KSC∏i=1(μQCQTLRP−j)αSC−iei2π(∏KSCi=1(μQCQTLIP−j)αSC−i),(1−KSC∏i=1(1−ηqCQQCQTLRP−j)αSC−i)1qCQei2π(1−∏KSCi=1(1−ηqCQQCQTLIP−j)αSC−i)1qCQ)) |
∑1≤j1≤⋯≤jKSCKSC∏i=1QαSC−iCQTL−ji=(ΔLT(∑1≤j1≤⋯≤jKSCKSC∏i=1(Δ−1LT(sSLT−ji,αSC−ji))αSC−i),((1−∏1≤j1≤⋯≤jKSC(1−KSC∏i=1(μqSCQCQTLRP−j)αSC−i))1qSCei2π(1−∏1≤j1≤⋯≤jKSC(1−∏KSCi=1(μqSCQCQTLIP−j)αSC−i))1qSC,∏1≤j1≤⋯≤jKSC(1−KSC∏i=1(1−ηqCQQCQTLRP−j)αSC−i)1qCQei2π(∏1≤j1≤⋯≤jKSC(1−∏KSCi=1(1−ηqCQQCQTLIP−j)αSC−i)1qCQ))) |
∑1≤j1≤⋯≤jKSC∏KSCi=1QαSC−iCQTL−jiCKSCn=(ΔLT(∑1≤j1≤⋯≤jKSC∏KSCi=1(Δ−1LT(sSLT−ji,αSC−ji))αSC−iCKSCn),((1−∏1≤j1≤⋯≤jKSC(1−KSC∏i=1(μqCQQCQTLRP−j)αSC−i)1CKSCn)1qCQei2π(1−∏1≤j1≤⋯≤jKSC(1−∏KSCi=1(μqCQQCQTLIP−j)αSC−i)1CKSCn)1qCQ,(∏1≤j1≤⋯≤jKSC(1−KSC∏i=1(1−ηqCQQCQTLRP−j)αSC−i)1CKSCn)1qCQei2π(∏1≤j1≤⋯≤jKSC(1−∏KSCi=1(1−ηqCQQCQTLIP−j)αSC−i)1CKSCn)1qCQ)) |
(∑1≤j1≤⋯≤jKSC∏KSCi=1QαSC−iCQTL−jiCKSCn)1αSC−1+αSC−2+⋯+αSC−KSC=(ΔLT((∑1≤j1≤⋯≤jKSC∏KSCi=1(Δ−1LT(sSLT−ji,αSC−ji))αSC−iCKSCn)1αSC−1+αSC−2+⋯+αSC−KSC),(((1−∏1≤j1≤⋯≤jKSC(1−KSC∏i=1(μqCQQCQTLRP−j)αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQ×ei2π(((1−∏1≤j1≤⋯≤jKSC(1−∏KSCi=1(μqCQQCQTLIP−j)αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQ),(1−(1−∏1≤j1≤⋯≤jKSC(1−KSC∏i=1(1−ηqCQQCQTLRP−j)αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQ×ei2π(1−(1−∏1≤j1≤⋯≤jKSC(1−∏KSCi=1(1−ηqCQQCQTLIP−j)αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQ)) |
Furthermore, by using the investigated operators, we discuss certain properties such as idempotency, commutativity, monotonicity, and boundedness, which are very important for the proposed work.
Theorem 5.3. For the family of CQRO2-TLVs
QCQTL−j=((sSLT−j,αSC−j),(μQCQTLRP−jei2π(μQCQTLIP−j),ηQCQTLRP−jei2π(ηQCQTLIP−j)))(j=1,2,3,…,n), then
(1). QCQTL−j=QCQTL=((sSLT,αSC),(μQCQTLRPei2π(μQCQTLIP),ηQCQTLRPei2π(ηQCQTLIP))), implies CQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(QCQTL−1,QCQTL−2,…,QCQTL−n) =QCQTL.
(2). if QCQTL−j is a collection of CQRO2-TLVs and Q'CQTL−j is any replacement of QCQTL−j, then CQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(QCQTL−1,QCQTL−2,…,QCQTL−n)=CQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(Q'CQTL−1,Q'CQTL−2,…,Q'CQTL−n).
(3). if QCQTL−j and Q'CQTL−j are any two collections of CQRO2-TLVs with a situations s.t.QCQTL−j≤Q'CQTL−j,
then CQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(QCQTL−1,QCQTL−2,…,QCQTL−n)≤CQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(Q'CQTL−1,Q'CQTL−2,…,Q'CQTL−n).
(4). if QCQTL−j=((sSLT−j,αSC−j),(μQCQTLRP−jei2π(μQCQTLIP−j),ηQCQTLRP−jei2π(ηQCQTLIP−j))) is a family of the CQRO2-TLVs, then
min(QCQTL−1,QCQTL−2,…,QCQTL−n)≤CQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(QCQTL−1,QCQTL−2,…,QCQTL−n)≤max(QCQTL−1,QCQTL−2,…,QCQTL−n) |
Proof.
(1). If QCQTL=((sSLT,αSC),(μQCQTLRPei2π(μQCQTLIP),ηQCQTLRPei2π(ηQCQTLIP))), then we have
CQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(QCQTL−1,QCQTL−2,…,QCQTL−n)=(ΔLT((∑1≤j1≤⋯≤jKSC∏KSCi=1(Δ−1LT(sSLT−ji,αSC−ji))αSC−iCKSCn)1αSC−1+αSC−2+⋯+αSC−KSC),(((1−∏1≤j1≤⋯≤jKSC(1−KSC∏i=1(μqCQQCQTLRP−j)αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQ×ei2π(((1−∏1≤j1≤⋯≤jKSC(1−∏KSCi=1(μqCQQCQTLIP−j)αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQ),(1−(1−∏1≤j1≤⋯≤jKSC(1−KSC∏i=1(1−ηqCQQCQTLRP−j)αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQ×ei2π(1−(1−∏1≤j1≤⋯≤jKSC(1−∏KSCi=1(1−ηqCQQCQTLIP−j)αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQ))=(ΔLT((∑1≤j1≤⋯≤jKSC∏KSCi=1(Δ−1LT(sSLT,αSC))αSC−iCKSCn)1αSC−1+αSC−2+⋯+αSC−KSC),(((1−∏1≤j1≤⋯≤jKSC(1−KSC∏i=1(μqCQQCQTLRP)αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQ×ei2π(((1−∏1≤j1≤⋯≤jKSC(1−∏KSCi=1(μqCQQCQTLIP)αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQ),(1−(1−∏1≤j1≤⋯≤jKSC(1−KSC∏i=1(1−ηqCQQCQTLRP)αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQ×ei2π(1−(1−∏1≤j1≤⋯≤jKSC(1−∏KSCi=1(1−ηqCQQCQTLIP)αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQ)) |
=(ΔLT(((Δ−1LT(sSLT,αSC))αSC−iCKSCn)1αSC−1+αSC−2+⋯+αSC−KSC),(((1−(1−(μqCQQCQTLRP)αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQei2π((1−(1−(μqCQQCQTLIP)αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQ,(1−(1−(1−(1−ηqCQQCQTLRP)αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQ×ei2π(1−(1−(1−(1−ηqCQQCQTLIP)αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQ))=((sSLT,αSC),(μQCQTLRPei2π(μQCQTLIP),ηQCQTLRPei2π(ηQCQTLIP)))=QCQTL. |
(2). By supposition, we have QCQTL−j, a collection CQRO2-TLVs and Q'CQTL−j is a slight substitution of QCQTL−j, then
CQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(QCQTL−1,QCQTL−2,…,QCQTL−n)=(∑1≤j1≤⋯≤jKSC∏KSCi=1QαSC−iCQTL−jiCKSCn)1αSC−1+αSC−2+⋯+αSC−KSC=(∑1≤j1≤⋯≤jKSC∏KSCi=1Q'αSC−iCQTL−jiCKSCn)1αSC−1+αSC−2+⋯+αSC−KSC=CQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(Q'CQTL−1,Q'CQTL−2,…,Q'CQTL−n). |
(3). By hypothesis, we have if QCQTL−j and Q'CQTL−j are any two collectionss of CQRO2-TLVs with the settings s.t. QCQTL−j≤Q'CQTL−j, then
KSC∏i=1QαSC−iCQTL−ji≤KSC∏i=1Q'αSC−iCQTL−ji⟹∑1≤j1≤⋯≤jKSCKSC∏i=1QαSC−iCQTL−ji≤∑1≤j1≤⋯≤jKSCKSC∏i=1Q'αSC−iCQTL−ji⟹∑1≤j1≤⋯≤jKSC∏KSCi=1QαSC−iCQTL−jiCKSCn≤∑1≤j1≤⋯≤jKSC∏KSCi=1Q'αSC−iCQTL−jiCKSCn⟹(∑1≤j1≤⋯≤jKSC∏KSCi=1QαSC−iCQTL−jiCKSCn)1αSC−1+αSC−2+⋯+αSC−KSC≤(∑1≤j1≤⋯≤jKSC∏KSCi=1Q'αSC−iCQTL−jiCKSCn)1αSC−1+αSC−2+⋯+αSC−KSC. |
Hence
CQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(QCQTL−1,QCQTL−2,…,QCQTL−n)≤CQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(Q'CQTL−1,Q'CQTL−2,…,Q'CQTL−n). |
(4). By hypothesis, if we have
QCQTL−j=((sSLT−j,αSC−j),(μQCQTLRP−jei2π(μQCQTLIP−j),ηQCQTLRP−jei2π(ηQCQTLIP−j))), |
a collection of the CQRO2-TLVs, Q−CQTL−j=min(QCQTL−1,QCQTL−2,…,QCQTL−n) and Q+CQTL−j=max(QCQTL−1,QCQTL−2,…,QCQTL−n), then by means of the properties (1) & (3), we have
CQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(QCQTL−1,QCQTL−2,…,QCQTL−n)≥CQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(Q−CQTL−1,Q−CQTL−2,…,Q−CQTL−n)=Q−CQTL |
CQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(QCQTL−1,QCQTL−2,…,QCQTL−n)≤CQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(Q+CQTL−1,Q+CQTL−2,…,Q+CQTL−n)=Q+CQTL. |
Hence
min(QCQTL−1,QCQTL−2,…,QCQTL−n)≤CQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(QCQTL−1,QCQTL−2,…,QCQTL−n)≤max(QCQTL−1,QCQTL−2,…,QCQTL−n). |
Definition 5.4. For the family of CQRO2-TLVs QQTL−j(j=1,2,3,…,n), the WGMSM operator is given by:
WCQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(QCQTL−1,QCQTL−2,…,QCQTL−n)=(∑1≤j1≤⋯≤jKSC∏KSCi=1(ΩWV−jiQCQTL−ji)αSC−iCKSCn)1αSC−1+αSC−2+⋯+αSC−KSC | (5.3) |
where KSC=1,2,…,n,αSC−1,αSC−2,…,αSC−KSC≥0,(j1,j2,…,jKSC) represents the K-tuple collection of (1,2,..,n), and ΩWV=(ΩWV−1,ΩWV−2,…,ΩWV−n)T with the condition ∑nj=1ΩWV−j=1.
Theorem 5.5. For the family of CQRO2-TLVs
QCQTL−j=((sSLT−j,αSC−j),(μQCQTLRP−jei2π(μQCQTLIP−j),ηQCQTLRP−jei2π(ηQCQTLIP−j)))(j=1,2,3,…,n), |
WCQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(QCQTL−1,QCQTL−2,…,QCQTL−n)=(ΔLT((∑1≤j1≤⋯≤jKSC∏KSCi=1(ΩWV−jiΔ−1LT(sSLT−ji,αSC−ji))αSC−iCKSCn)1αSC−1+αSC−2+⋯+αSC−KSC),(((1−∏1≤j1≤⋯≤jKSC(1−∏KSCi=1(1−(1−μqCQQCQTLRP−j)ΩWV−ji)αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQ×ei2π((1−∏1≤j1≤⋯≤jKSC(1−∏KSCi=1(1−(1−μqCQQCQTLIP−j)ΩWV−ji)αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQ,(1−(1−∏1≤j1≤⋯≤jKSC(1−∏KSCi=1(1−ηΩWV−jiqCQQCQTLRP−j(ử))αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQ×ei2π(1−(1−∏1≤j1≤⋯≤jKSC(1−∏KSCi=1(1−ηΩWV−jiqCQQCQTLIP−j(ử))αSC−i)1CKSCn)1αSC−1+αSC−2+⋯+αSC−KSC)1qCQ)). | (5.4) |
Proof. Straightforward.
Theorem 5.6. For the family of CQROF2-TLVs
QCQTL−j=((sSLT−j,αSC−j),(μQCQTLRP−jei2π(μQCQTLIP−j),ηQCQTLRP−jei2π(ηQCQTLIP−j)))(j=1,2,3,…,n), |
(1). if QCQTL−j=QCQTL=((sSLT,αSC),(μQCQTLRPei2π(μQCQTLIP),ηQCQTLRPei2π(ηQCQTLIP))), then WCQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(QCQTL−1,QCQTL−2,…,QCQTL−n)=QCQTL.
(2). if QCQTL−j is a collection CQRO2-TLVs & Q'CQTL−j is a replacement for QCQTL−j, then
WCQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(QCQTL−1,QCQTL−2,…,QCQTL−n)=WCQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(Q'CQTL−1,Q'CQTL−2,…,Q'CQTL−n). |
(3). if QCQTL−j and Q'CQTL−j are two collections of CQRO2-TLVs with the settings s.t. QCQTL−j≤Q'CQTL−j, then
WCQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(QCQTL−1,QCQTL−2,…,QCQTL−n)≤WCQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(Q'CQTL−1,Q'CQTL−2,…,Q'CQTL−n). |
(4). if QCQTL−j=((sSLT−j,αSC−j),(μQCQTLRP−jei2π(μQCQTLIP−j),ηQCQTLRP−jei2π(ηQCQTLIP−j))) is a family of the CQRO2-TLVs, then
min(QCQTL−1,QCQTL−2,…,QCQTL−n)≤WCQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(QCQTL−1,QCQTL−2,…,QCQTL−n)≤max(QCQTL−1,QCQTL−2,…,QCQTL−n). |
Proof. Straightforward.
We explored the LF based on CQRO2-TLVs and 3WD for CQRO2-TLVs, where the probability vector is represented by: AAC={χPAC,χBAC,χNAC}, ΩS={FB,∼FNB} and
D={Pr(FB|[ử]),Pr(∼FNB|[ử])} with Pr(FB|[ử])+Pr(∼FNB|[ử])=1. Then, we have the following:
Step 1: By using the Eqs (6.1)–(6.3), we examine the LFs, which are stated below:
QCQTL−−QCQ−PACPAC=((sSLT(−QCQ−PACPAC),αSC),(μQCQTLRP(−QCQ−PACPAC)ei2π(μQCQTLIP(−QCQ−PACPAC)),ηQCQTLRP(−QCQ−PACPAC)ei2π(ηQCQTLIP(−QCQ−PACPAC))))andQCQTL−−QCQ−BACPAC=((sSLT(−QCQ−BACPAC),αSC),(μQCQTLRP(−QCQ−BACPAC)ei2π(μQCQTLIP(−QCQ−BACPAC)),ηQCQTLRP(−QCQ−BACPAC)ei2π(ηQCQTLIP(−QCQ−BACPAC)))); | (6.1) |
QCQTL−−QCQ−NACPAC=((sSLT(−QCQ−NACPAC),αSC),(μQCQTLRP(−QCQ−NACPAC)ei2π(μQCQTLIP(−QCQ−NACPAC)),ηQCQTLRP(−QCQ−NACPAC)ei2π(ηQCQTLIP(−QCQ−NACPAC))))andQCQTL−−QCQ−PACNAC=((sSLT(−QCQ−PACNAC),αSC),(μQCQTLRP(−QCQ−PACNAC)ei2π(μQCQTLIP(−QCQ−PACNAC)),ηQCQTLRP(−QCQ−PACNAC)ei2π(ηQCQTLIP(−QCQ−PACNAC)))); | (6.2) |
QCQTL−−QCQ−BACNAC=((sSLT(−QCQ−BACNAC),αSC),(μQCQTLRP(−QCQ−BACNAC)ei2π(μQCQTLIP(−QCQ−BACNAC)),ηQCQTLRP(−QCQ−BACNAC)ei2π(ηQCQTLIP(−QCQ−BACNAC))))andQCQTL−−QCQ−NACNAC=((sSLT(−QCQ−NACNAC),αSC),(μQCQTLRP(−QCQ−NACNAC)ei2π(μQCQTLIP(−QCQ−NACNAC)),ηQCQTLRP(−QCQ−NACNAC)ei2π(ηQCQTLIP(−QCQ−NACNAC)))). | (6.3) |
Step 2: By using the Eq (6.4), we aggregate the decision matrix which is construct by decision experts.
WCQRO2−TLGMSM(KSC,αSC−1,αSC−2,…,αSC−KSC)(Q1CQTL−ij,Q2CQTL−ij,…,QnCQTL−ij)=QCQTL−ij. | (6.4) |
Step 3: By using the Eqs (6.5)–(6.7), we examine the expected losses YEL(χjAC|[ử]),j=P,B,N and the different actions are expressed below:
YEL(χPAC|[ử])=QCQTL−−QCQ−PACPACPr(FB|[ử])⊕CQTLQCQTL−−QCQ−PACPACPr(∼FNB|[ử]) | (6.5) |
YEL(χBAC|[ử])=QCQTL−−QCQ−BACPACPr(FB|[ử])⊕CQTLQCQTL−−QCQ−BACNACPr(∼FNB|[ử]) | (6.6) |
YEL(χNAC|[ử])=QCQTL−−QCQ−NACPACPr(FB|[ử])⊕CQTLQCQTL−−QCQ−NACNACPr(∼FNB|[ử]) | (6.7) |
Step 4: By using the Eqs (6.8)–(6.10), we examine the expected values, which are stated below:
QEV(YEL(χPAC|[ử]))=((δB×Δ−1LT(sSLT(−QCQ−PACPAC),αSC)+δNB×Δ−1LT(sSLT(−QCQ−PACNAC),αSC))×((1−(1−μqCQQCQTLRP(−QCQ−PACPAC))δB(1−μqCQQCQTLRP(−QCQ−PACNAC))δNB)1qCQ+(1−(1−μqCQQCQTLIP(−QCQ−PACPAC))δB(1−μqCQQCQTLIP(−QCQ−PACNAC))δNB)1qCQ−(ηQCQTLRP(−QCQ−PACPAC))δB(ηQCQTLRP(−QCQ−PACNAC))δNB−(ηQCQTLRP(−QCQ−PACPAC))δB(ηQCQTLRP(−QCQ−PACNAC))δNB))8, | (6.8) |
QEV(YEL(χBAC|[ử]))=((δB×Δ−1LT(sSLT(−QCQ−BACPAC),αSC)+δNB×Δ−1LT(sSLT(−QCQ−BACNAC),αSC))×((1−(1−μqCQQCQTLRP(−QCQ−BACPAC))δB(1−μqCQQCQTLRP(−QCQ−BACNAC))δNB)1qCQ+(1−(1−μqCQQCQTLIP(−QCQ−BACPAC))δB(1−μqCQQCQTLIP(−QCQ−BACNAC))δNB)1qCQ−(ηQCQTLRP(−QCQ−BACPAC))δB(ηQCQTLRP(−QCQ−BACNAC))δNB−(ηQCQTLRP(−QCQ−BACPAC))δB(ηQCQTLRP(−QCQ−BACNAC))δNB))8, | (6.9) |
QEV(YEL(χDAC|[ử]))=((δB×Δ−1LT(sSLT(−QCQ−NACPAC),αSC)+δNB×Δ−1LT(sSLT(−QCQ−NACNAC),αSC))×((1−(1−μqCQQCQTLRP(−QCQ−NACPAC))δB(1−μqCQQCQTLRP(−QCQ−NACNAC))δNB)1qCQ+(1−(1−μqCQQCQTLIP(−QCQ−NACPAC))δB(1−μqCQQCQTLIP(−QCQ−NACNAC))δNB)1qCQ−(ηQCQTLRP(−QCQ−NACPAC))δB(ηQCQTLRP(−QCQ−NACNAC))δNB−(ηQCQTLRP(−QCQ−NACPAC))δB(ηQCQTLRP(−QCQ−NACNAC))δNB))8. | (6.10) |
Moreover, we investigate the accuracy function, which is stated below:
GAF(YEL(χPAC|[ử]))=((δB×Δ−1LT(sSLT(−QCQ−PACPAC),αSC)+δNB×Δ−1LT(sSLT(−QCQ−PACNAC),αSC))×((1−(1−μqCQQCQTLRP(−QCQ−PACPAC))δB(1−μqCQQCQTLRP(−QCQ−PACNAC))δNB)1qCQ+(1−(1−μqCQQCQTLIP(−QCQ−PACPAC))δB(1−μqCQQCQTLIP(−QCQ−PACNAC))δNB)1qCQ+(ηQCQTLRP(−QCQ−PACPAC))δB(ηQCQTLRP(−QCQ−PACNAC))δNB+(ηQCQTLRP(−QCQ−PACPAC))δB(ηQCQTLRP(−QCQ−PACNAC))δNB))8, | (6.11) |
GAF(YEL(χBAC|[ử]))=((δB×Δ−1LT(sSLT(−QCQ−BACPAC),αSC)+δNB×Δ−1LT(sSLT(−QCQ−BACNAC),αSC))×((1−(1−μqCQQCQTLRP(−QCQ−BACPAC))δB(1−μqCQQCQTLRP(−QCQ−BACNAC))δNB)1qCQ+(1−(1−μqCQQCQTLIP(−QCQ−BACPAC))δB(1−μqCQQCQTLIP(−QCQ−BACNAC))δNB)1qCQ+(ηQCQTLRP(−QCQ−BACPAC))δB(ηQCQTLRP(−QCQ−BACNAC))δNB+(ηQCQTLRP(−QCQ−BACPAC))δB(ηQCQTLRP(−QCQ−BACNAC))δNB))8, | (6.12) |
GAF(YEL(χDAC|[ử]))=((δB×Δ−1LT(sSLT(−QCQ−NACPAC),αSC)+δNB×Δ−1LT(sSLT(−QCQ−NACNAC),αSC))×((1−(1−μqCQQCQTLRP(−QCQ−NACPAC))δB(1−μqCQQCQTLRP(−QCQ−NACNAC))δNB)1qCQ+(1−(1−μqCQQCQTLIP(−QCQ−NACPAC))δB(1−μqCQQCQTLIP(−QCQ−NACNAC))δNB)1qCQ+(ηQCQTLRP(−QCQ−NACPAC))δB(ηQCQTLRP(−QCQ−NACNAC))δNB+(ηQCQTLRP(−QCQ−NACPAC))δB(ηQCQTLRP(−QCQ−NACNAC))δNB))8. | (6.13) |
Step 5: By using the Eqs (6.14)–(6.16), we examine the three-way decision rules, which are listed below:
PAC−1:WhenQEV(YEL(χPAC|[ử]))≤GAF(YEL(χNAC|[ử])),thenử∈POS(FP); | (6.14) |
{B}_{AC-1} : \;{\rm{When}}\; {Q}_{EV}\left({Y}_{EL}\left({\chi }_{{B}_{AC}}\left|\right[ử]\right)\right)\le {G}_{AF}\left({Y}_{EL}\left({\chi }_{{N}_{AC}}\left|\right[ử]\right)\right) , \;{\rm{then}}\; ử\in BUN\left({\mathcal{F}}_{P}\right) ; | (6.15) |
{N}_{AC-1} : \;{\rm{When}}\; {Q}_{EV}\left({Y}_{EL}\left({\chi }_{{N}_{AC}}\left|\right[ử]\right)\right)\le {G}_{AF}\left({Y}_{EL}\left({\chi }_{{B}_{AC}}\left|\right[ử]\right)\right) , \;{\rm{then}}\; ử\in NEG\left({\mathcal{F}}_{P}\right) ; | (6.16) |
Step 6: This ends the proof.
Example 6.1. Three decision experts \left\{{ử}_{1}, {ử}_{2}, {ử}_{3}\right\} and {D}_{DE-k}(k = \mathrm{1, 2}, 3) with weight vectors {\mathrm{\Omega }}_{\mathcal{W}\mathcal{V}} = {\left(\mathrm{0.4, 0.35, 0.25}\right)}^{\boldsymbol{T}} are given. Then, \mathrm{Pr}\left({\mathcal{F}}_{B}\left|\right[{ử}_{j}]\right) = 0.3, j = 1, 2, 3, 4 .
Step 1: By using the Eqs (6.1)–(6.3), we examine the LFs of the Tables 3, 4, and 5, which are stated below:
{\mathrm{ử}}_{1} | {\mathrm{ử}}_{2} | |||
{\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | {\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | |
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{1}, 0.01\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.02\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.03\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.04\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{3}, 0.011\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.021\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{5}, 0.031\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.041\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{4}, 0.012\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}\\, 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.022\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.032\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.042\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) |
{\mathrm{ử}}_{3} | {\mathrm{ử}}_{4} | |||
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.013\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.023\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.033\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.04\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{2}, 0.014\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.024\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.034\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.043\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{3}, 0.015\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.025\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{3}, 0.035\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.044\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) |
{\bf{ử}}_{1} | {\bf{ử}}_{2} | |||
{\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | {\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | |
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.02\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.03\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.04\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{5}, 0.05\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{1}, 0.021\right), \\ \left(\begin{array}{c}0.81{e}^{i2\pi \left(0.81\right)}, \\ 0.11{e}^{i2\pi \left(0.11\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{3}, 0.031\right), \\ \left(\begin{array}{c}0.61{e}^{i2\pi \left(0.61\right)}, \\ 0.21{e}^{i2\pi \left(0.21\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.041\right), \\ \left(\begin{array}{c}0.1{e}^{i2\pi \left(0.1\right)}, \\ 0.41{e}^{i2\pi \left(0.41\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.01\right), \\ \left(\begin{array}{c}0.71{e}^{i2\pi \left(0.71\right)}, \\ 0.21{e}^{i2\pi \left(0.21\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{2}, 0.022\right), \\ \left(\begin{array}{c}0.82{e}^{i2\pi \left(0.82\right)}, \\ 0.12{e}^{i2\pi \left(0.12\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.032\right), \\ \left(\begin{array}{c}0.62{e}^{i2\pi \left(0.62\right)}, \\ 0.22{e}^{i2\pi \left(0.22\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.042\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.042\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) |
{\bf{ử}}_{3} | {\bf{ử}}_{4} | |||
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.03\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.04\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.03\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.04\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{5}, 0.031\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.041\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{3}, 0.031\right), \\ \left(\begin{array}{c}0.61{e}^{i2\pi \left(0.61\right)}, \\ 0.21{e}^{i2\pi \left(0.21\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.041\right), \\ \left(\begin{array}{c}0.1{e}^{i2\pi \left(0.1\right)}, \\ 0.41{e}^{i2\pi \left(0.41\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{4}, 0.032\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.042\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.032\right), \\ \left(\begin{array}{c}0.62{e}^{i2\pi \left(0.62\right)}, \\ 0.22{e}^{i2\pi \left(0.22\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.042\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) |
{\bf{ử}}_{1} | {\bf{ử}}_{2} | |||
{\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | {\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | |
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.013\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.023\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.033\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.04\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{2}, 0.014\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.024\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.034\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.043\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.03\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.04\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.03\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.04\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) |
{\bf{ử}}_{3} | {\bf{ử}}_{4} | |||
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.013\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.023\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.033\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.04\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.02\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.03\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.04\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{5}, 0.05\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{1}, 0.021\right), \\ \left(\begin{array}{c}0.81{e}^{i2\pi \left(0.81\right)}, \\ 0.11{e}^{i2\pi \left(0.11\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{3}, 0.031\right), \\ \left(\begin{array}{c}0.61{e}^{i2\pi \left(0.61\right)}, \\ 0.21{e}^{i2\pi \left(0.21\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.041\right), \\ \left(\begin{array}{c}0.1{e}^{i2\pi \left(0.1\right)}, \\ 0.41{e}^{i2\pi \left(0.41\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.01\right), \\ \left(\begin{array}{c}0.71{e}^{i2\pi \left(0.71\right)}, \\ 0.21{e}^{i2\pi \left(0.21\right)}\end{array}\right)\end{array}\right) |
{\bf{ử}}_{1} | {\bf{ử}}_{2} | |||
{\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | {\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | |
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.012\right), \\ \left(\begin{array}{c}0.299{e}^{i2\pi \left(0.299\right)}, \\ 0.678{e}^{i2\pi \left(0.678\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1.41}, 0.021\right), \\ \left(\begin{array}{c}0.275{e}^{i2\pi \left(0.275\right)}, \\ 0.675{e}^{i2\pi \left(0.675\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.031\right), \\ \left(\begin{array}{c}0.251{e}^{i2\pi \left(0.251\right)}, \\ 0.622{e}^{i2\pi \left(0.622\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1.39}, 0.042\right), \\ \left(\begin{array}{c}0.274{e}^{i2\pi \left(0.274\right)}, \\ 0.66{e}^{i2\pi \left(0.66\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0.72}, 0.0112\right), \\ \left(\begin{array}{c}0.293{e}^{i2\pi \left(0.293\right)}, \\ 0.632{e}^{i2\pi \left(0.632\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.76}, 0.022\right), \\ \left(\begin{array}{c}0.274{e}^{i2\pi \left(0.274\right)}, \\ 0.606{e}^{i2\pi \left(0.606\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.85}, 0.033\right), \\ \left(\begin{array}{c}0.274{e}^{i2\pi \left(0.274\right)}, \\ 0.656{e}^{i2\pi \left(0.656\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.74}, 0.043\right), \\ \left(\begin{array}{c}0.269{e}^{i2\pi \left(0.269\right)}, \\ 0.659{e}^{i2\pi \left(0.659\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{1.04}, 0.013\right), \\ \left(\begin{array}{c}0.34{e}^{i2\pi \left(0.34\right)}, \\ 0.599{e}^{i2\pi \left(0.599\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.18}, 0.024\right), \\ \left(\begin{array}{c}0.318{e}^{i2\pi \left(0.318\right)}, \\ 0.563{e}^{i2\pi \left(0.563\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1.41}, 0.032\right), \\ \left(\begin{array}{c}0.297{e}^{i2\pi \left(0.297\right)}, \\ 0.657{e}^{i2\pi \left(0.657\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.14}, 0.042\right), \\ \left(\begin{array}{c}0.318{e}^{i2\pi \left(0.318\right)}, \\ 0.619{e}^{i2\pi \left(0.619\right)}\end{array}\right)\end{array}\right) |
{\mathrm{ử}}_{3} | {\mathrm{ử}}_{4} | |||
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.0142\right), \\ \left(\begin{array}{c}0.279{e}^{i2\pi \left(0.279\right)}, \\ 0.56{e}^{i2\pi \left(0.56\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1.443}, 0.0221\right), \\ \left(\begin{array}{c}0.25{e}^{i2\pi \left(0.25\right)}, \\ 0.75{e}^{i2\pi \left(0.75\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.0321\right), \\ \left(\begin{array}{c}0.21{e}^{i2\pi \left(0.21\right)}, \\ 0.62{e}^{i2\pi \left(0.62\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1.59}, 0.043\right), \\ \left(\begin{array}{c}0.254{e}^{i2\pi \left(0.254\right)}, \\ 0.70{e}^{i2\pi \left(0.70\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0.69}, 0.013\right), \\ \left(\begin{array}{c}0.288{e}^{i2\pi \left(0.288\right)}, \\ 0.612{e}^{i2\pi \left(0.612\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.81}, 0.023\right), \\ \left(\begin{array}{c}0.287{e}^{i2\pi \left(0.287\right)}, \\ 0.599{e}^{i2\pi \left(0.599\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.81}, 0.032\right), \\ \left(\begin{array}{c}0.257{e}^{i2\pi \left(0.257\right)}, \\ 0.670{e}^{i2\pi \left(0.670\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.57}, 0.0434\right), \\ \left(\begin{array}{c}0.273{e}^{i2\pi \left(0.273\right)}, \\ 0.69{e}^{i2\pi \left(0.69\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{1.31}, 0.023\right), \\ \left(\begin{array}{c}0.349{e}^{i2\pi \left(0.349\right)}, \\ 0.615{e}^{i2\pi \left(0.615\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.78}, 0.029\right), \\ \left(\begin{array}{c}0.389{e}^{i2\pi \left(0.389\right)}, \\ 0.569{e}^{i2\pi \left(0.569\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1.84}, 0.038\right), \\ \left(\begin{array}{c}0.302{e}^{i2\pi \left(0.302\right)}, \\ 0.686{e}^{i2\pi \left(0.686\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.35}, 0.0423\right), \\ \left(\begin{array}{c}0.319{e}^{i2\pi \left(0.319\right)}, \\ 0.617{e}^{i2\pi \left(0.617\right)}\end{array}\right)\end{array}\right) |
Step 2: Consider Eq (6.4), for {K}_{SC} = 3 , and the values of {\alpha }_{SC-1} = {\alpha }_{SC-2} = {\alpha }_{SC-3} = 1 , we have Table 6.
Step 3: By using the Eqs (6.5)–(6.7), we examine the expected losses {Y}_{EL}\left({\chi }_{{j}_{AC}}\left|\right[ử]\right), j = P, B, N , for {\delta }_{B-j} = 0.4, j = \mathrm{1, 2}, 3 and {q}_{SC} = 1 , and the separate actions are expressed and discussed in Table 7.
Symbols | {\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right) | {\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right) | {\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right) |
{\boldsymbol{ử}}_{1} | \left(\begin{array}{c}\left({s}_{0}, 0.1866\right), \\ \left(\begin{array}{c}0.2504{e}^{i2\pi \left(0.2504\right)}, \\ 0.6762{e}^{i2\pi \left(0.6762\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.1656\right), \\ \left(\begin{array}{c}0.2817{e}^{i2\pi \left(0.2817\right)}, \\ 0.6163{e}^{i2\pi \left(0.6163\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.1244\right), \\ \left(\begin{array}{c}0.3269{e}^{i2\pi \left(0.3269\right)}, \\ 0.5771{e}^{i2\pi \left(0.5771\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{ử}}_{2} | \left(\begin{array}{c}\left({s}_{1}, 0.0044\right), \\ \left(\begin{array}{c}0.2649{e}^{i2\pi \left(0.2649\right)}, \\ 0.6445{e}^{i2\pi \left(0.6445\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.1346\right), \\ \left(\begin{array}{c}0.271{e}^{i2\pi \left(0.271\right)}, \\ 0.6578{e}^{i2\pi \left(0.6578\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.1676\right), \\ \left(\begin{array}{c}0.3097{e}^{i2\pi \left(0.3097\right)}, \\ 0.6339{e}^{i2\pi \left(0.6339\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{ử}}_{3} | \left(\begin{array}{c}\left({s}_{0}, 0.1921\right), \\ \left(\begin{array}{c}0.2617{e}^{i2\pi \left(0.2617\right)}, \\ 0.6673{e}^{i2\pi \left(0.6673\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.1714\right), \\ \left(\begin{array}{c}0.2874{e}^{i2\pi \left(0.2874\right)}, \\ 0.6042{e}^{i2\pi \left(0.6042\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.025\right), \\ \left(\begin{array}{c}0.3733{e}^{i2\pi \left(0.3733\right)}, \\ 0.587{e}^{i2\pi \left(0.587\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{ử}}_{4} | \left(\begin{array}{c}\left({s}_{1}, 0.0166\right), \\ \left(\begin{array}{c}0.2367{e}^{i2\pi \left(0.2367\right)}, \\ 0.6668{e}^{i2\pi \left(0.6668\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.172\right), \\ \left(\begin{array}{c}0.2666{e}^{i2\pi \left(0.2666\right)}, \\ 0.6819{e}^{i2\pi \left(0.6819\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.192\right), \\ \left(\begin{array}{c}0.3123{e}^{i2\pi \left(0.3123\right)}, \\ 0.6437{e}^{i2\pi \left(0.6437\right)}\end{array}\right)\end{array}\right) |
Step 4: By using the Eqs (6.8)–(6.10), we examine the expected values, which are stated in Table 8.
Symbols | {\boldsymbol{Q}}_{\boldsymbol{E}\boldsymbol{V}}\left({\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right)\right) | {\boldsymbol{Q}}_{\boldsymbol{E}\boldsymbol{V}}\left({\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right)\right) | {\boldsymbol{Q}}_{\boldsymbol{E}\boldsymbol{V}}\left({\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right)\right) |
{\boldsymbol{ử}}_{1} | 0.0137 | 0.017 | 0.0119 |
{\boldsymbol{ử}}_{2} | 0.0185 | 0.0096 | 0.0095 |
{\boldsymbol{ử}}_{3} | 0.0136 | 0.0186 | 0.0089 |
{\boldsymbol{ử}}_{4} | 0.0211 | 0.0088 | 0.0085 |
When the predictable values are unsuccessful in catching the relationships amongst any two predictable losses, we discover the concepts of accuracy function, which is quantified in Table 9.
Symbols | {\boldsymbol{G}}_{\boldsymbol{A}\boldsymbol{F}}\left({\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right)\right) | {\boldsymbol{G}}_{\boldsymbol{A}\boldsymbol{F}}\left({\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right)\right) | {\boldsymbol{G}}_{\boldsymbol{A}\boldsymbol{F}}\left({\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right)\right) |
{\boldsymbol{ử}}_{1} | 0.266 | 0.2222 | 0.1555 |
{\boldsymbol{ử}}_{2} | 0.282 | 0.1867 | 0.2219 |
{\boldsymbol{ử}}_{3} | 0.27 | 0.2257 | 0.2731 |
{\boldsymbol{ử}}_{4} | 0.3127 | 0.2435 | 0.2656 |
Step 5: By using the Eqs (6.11)–(6.13), we examine the three-way decision rules, as discussed in Table 10.
Enterprises | Decision rule |
{\boldsymbol{ử}}_{1} | {P}_{AC-1} |
{\boldsymbol{ử}}_{2} | {P}_{AC-1} |
{\boldsymbol{ử}}_{3} | {P}_{AC-1} |
{\boldsymbol{ử}}_{4} | {P}_{AC-1} |
Step 6: This ends the proof.
The obtained result states that all these alternatives belong to positive opinions, which are {P}_{AC-1} . Furthermore, the comparison of the explored work with some existing work is discussed in Table 11.
Enterprises | {\boldsymbol{ử}}_{1} | {\boldsymbol{ử}}_{2} | {\boldsymbol{ử}}_{3} | {\boldsymbol{ử}}_{4} |
Proposed work for q=1 | {P}_{AC-1} | {P}_{AC-1} | {P}_{AC-1} | {P}_{AC-1} |
Proposed work for q=2 | {P}_{AC-1} | {P}_{AC-1} | {P}_{AC-1} | {P}_{AC-1} |
Proposed work for q=3 | {P}_{AC-1} | {P}_{AC-1} | {P}_{AC-1} | {P}_{AC-1} |
From the above analysis, we conclude that all approaches have provided similar consequences and are exposed in Table 11; additionally, all alternatives belong to the +ve regions. The graphical interpretation for the information's score and the expected positive, boundary, and negative values of Table 8 and Table 9 are shown in Figure 4 and Figure 5, respectively.
In the explored work, if we choose the values of q = 1, 2 and the imaginary part is zero, then the explored work is reduced for intuitionistic 2-tuple and Pythagorean 2-tuple linguistic sets. Similarly, if we choose the values of q = 1, 2, then the explored will be reduced for complex intuitionistic 2-tuple and complex Pythagorean 2-tuple linguistic sets. The presented approach is more powerful and more proficient than the existing ones, as given in [34,35,36,37].
We modified the notions of 3WD and DTRS in the environment of CQRO2-TLV and elaborated certain important properties. Moreover, GMSM is a dominant and more flexible method to determine the accuracy and dominancy of real life issues. Therefore, by considering the CQRO2-TL information and GMSM, we presented CQRO2-TLGMSM operator and the WCQRO2-TLGMSM operator, and demonstrated their effective properties. We also elaborated a q-rung orthopair 2-tuple linguistic DTRS model and discussed its applications. Furthermore, we discussed some important and well known properties of the defined aggregation operators like idempotency, commutativity, monotonicity, and boundedness. We discussed some examples to explain our proposed methods and techniques. To prove the authenticity, workability, effectiveness, and supremacy of our proposed methods, techniques, and notions, we initiated a comparative analysis and proved that our initiated notions are much better as compared to certain existing notions.
In the future, we will discuss the proposed notions for CQRO2-TLVSs in the framework of complex q-rung orthopair fuzzy sets [38], picture hesitant fuzzy sets [39,40], neutrosophic sets [41,42], and some more useful frameworks and notions, as given in [43,44,45,46,47,48,49].
Researchers Supporting Project number (RSP-2021/244), King Saud University, Riyadh, Saudi Arabia.
The authors declare no conflicts of interest about the publication of the research article.
[1] |
N. U. Prabhu, On the ruin problem of collective risk theory, Ann. Math. Stat., 32 (1961), 757–764. https://doi.org/10.1214/aoms/1177704970 doi: 10.1214/aoms/1177704970
![]() |
[2] |
M. I. Taksar, Optimal risk and dividend distribution control models for an insur- ance company, Math. Methods Oper. Res., 51 (2000), 1–42. https://doi.org/10.1007/s001860050001 doi: 10.1007/s001860050001
![]() |
[3] |
W. Yu, P. Guo, Q. Wang, G. Guan, Q. Yang, Y. Huang, et al., On a periodic capital injection and barrier dividend strategy in the compound Poisson risk model, Mathematics, 8 (2020), 511. https://doi.org/10.3390/math8040511 doi: 10.3390/math8040511
![]() |
[4] |
H. U. Gerber, E. S. W. Shiu, On optimal dividend strategies in the compound Poisson model, N. Am. Actuar. J., 10 (2006), 76–93. https://doi.org/10.1080/10920277.2006.10596249 doi: 10.1080/10920277.2006.10596249
![]() |
[5] |
H. Yuan, Y. Hu, Optimal investment for an insurer under liquid reserves, J. Ind. Manage. Optim., 17 (2020), 339–355. https://doi.org/10.3934/jimo.2019114 doi: 10.3934/jimo.2019114
![]() |
[6] |
B. Sundt, J. L. Teugels, Ruin estimates under interest force, Insur. Math. Econ., 16 (1995), 7–22. https://doi.org/10.1016/0167-6687(94)00023-8 doi: 10.1016/0167-6687(94)00023-8
![]() |
[7] |
Y. Fang, R. Wu, Optimal dividend strategy in the compound poisson model with constant interest, Stoch. Models, 23 (2007), 149–166. https://doi.org/10.1080/15326340601142271 doi: 10.1080/15326340601142271
![]() |
[8] |
J. Cai, R. Feng, G. E. Willmot, Analysis of the compound Poisson surplus model with liquid reserves, interest and dividends, ASTIN Bull., 39 (2009), 225–247. https://doi.org/10.2143/AST.39.1.2038063 doi: 10.2143/AST.39.1.2038063
![]() |
[9] |
L. Yang, C. He, Absolute ruin in the compound Poisson model with credit and debit interests and liquid reserves, Appl. Stoch. Models Bus. Ind., 30 (2014), 157–171. https://doi.org/10.1002/asmb.1953 doi: 10.1002/asmb.1953
![]() |
[10] |
X. Chen, H. Ou, A compound Poisson risk model with proportional investment, J. Comput. Appl. Math., 242 (2013), 248–260. https://doi.org/10.1016/j.cam.2012.10.027 doi: 10.1016/j.cam.2012.10.027
![]() |
[11] |
C. Yin, K. C. Yuen, Optimality of the threshold dividend strategy for the compound poisson model, Stat. Probab. Lett., 81 (2011), 1841–1846. https://doi.org/10.1016/j.spl.2011.07.022 doi: 10.1016/j.spl.2011.07.022
![]() |
[12] |
X. S. Lin, K. P. Pavlova, The compound Poisson risk model with a threshold dividend strategy, Insur. Math. Econ., 38 (2006), 57–80. https://doi.org/10.1016/j.insmatheco.2005.08.001 doi: 10.1016/j.insmatheco.2005.08.001
![]() |
[13] |
N. Wan, Dividend payments with a threshold strategy in the compound poisson risk model perturbed by diffusion, Insur. Math. Econ., 40 (2007), 509–523. https://doi.org/10.1016/j.insmatheco.2006.08.002 doi: 10.1016/j.insmatheco.2006.08.002
![]() |
[14] | B. De Finetti, Su un'impostazione alternativa della teoria collettiva del rischio, In: Transactions of the XVth international congress of Actuaries, 2 (1957), 433–443. |
[15] |
J. Paulsen, H. K. Gjessing, Ruin theory with stochastic return on investments, Adv. Appl. Probab., 29 (1997), 965–985. https://doi.org/10.2307/1427849 doi: 10.2307/1427849
![]() |
[16] |
X. S. Lin, K. P. Sendova, The compound Poisson risk model with multiple thresholds, Insur. Math. Econ., 42 (2008), 617–627. https://doi.org/10.1016/j.insmatheco.2007.06.008 doi: 10.1016/j.insmatheco.2007.06.008
![]() |
[17] |
Z. Zhang, X. Han, The compound Poisson risk model under a mixed dividend strategy, Appl. Math. Comput., 315 (2017), 1–12. https://doi.org/10.1016/j.amc.2017.07.048 doi: 10.1016/j.amc.2017.07.048
![]() |
[18] | Y. Zhang, L. Mao, B. Kou, A perturbed risk model with liquid reserves, credit and debit interests and dividends under absolute ruin, In: Advances in computational science and computing, 2019. https://doi.org/10.1007/978-3-030-02116-0_40 |
[19] |
D. Peng, D. Liu, Z. Hou, Absolute ruin problems in a compound Poisson risk model with constant dividend barrier and liquid reserves, Adv. Differ. Equ., 2016 (2016), 72. https://doi.org/10.1186/s13662-016-0746-1 doi: 10.1186/s13662-016-0746-1
![]() |
[20] |
F. Dufresne, H. U. Gerber, Risk theory for the compound Poisson process that is perturbed by diffusion, Insur. Math. Econ., 10 (1991), 51–59. https://doi.org/10.1016/0167-6687(91)90023-Q doi: 10.1016/0167-6687(91)90023-Q
![]() |
[21] |
E. T. Whitaker, On the functions which are represented by the expansion of interpolating theory, Proc. Roy. Soc. Edinb., 35 (1915), 181–194. https://doi.org/10.1017/S0370164600017806 doi: 10.1017/S0370164600017806
![]() |
[22] | T. Carlson, J. Dockery, J. Lund, A sinc-collocation method for initial value problem, Math. Comput., 66 (1997), 215–235. |
[23] |
T. Okayama, Error estimates with explicit constants for the Sinc approximation over infinite intervals, Appl. Math. Comput., 319 (2018), 125–137. https://doi.org/10.1016/j.amc.2017.02.02 doi: 10.1016/j.amc.2017.02.02
![]() |
[24] |
K. Maleknejad, K. Nedaiasl, Application of Sinc-collocation method for solving a class of nonlinear Fredholm integral equations, Appl. Comput. Math. Appl., 62 (2011), 3292–3303. https://doi.org/10.1016/j.camwa.2011.08.045 doi: 10.1016/j.camwa.2011.08.045
![]() |
[25] |
C. Wang, N. Deng, S. Shen, Numerical method for a perturbed risk model with proportional investment, Mathematics, 11 (2022), 43. https://doi.org/10.1016/j.camwa.2011.08.045 doi: 10.1016/j.camwa.2011.08.045
![]() |
[26] | F. Stenger, Numerical methods based on sinc and analytic functions, New York: Springer-Verlag, 1993. https://doi.org/10.1007/978-1-4612-2706-9 |
[27] | F. Stenger, Handbook of sinc numerical methods, Boca Raton: CRC Press, 2011. https://doi.org/10.1201/b10375 |
[28] | J. Lund, K. L. Bowers, Sinc methods for quadrature and differential equations, SIAM, 1992. |
Symbols | {\mathcal{F}}_{\boldsymbol{B}}\left({\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}\right)=\boldsymbol{C}\boldsymbol{o}\boldsymbol{r}\boldsymbol{r}\boldsymbol{e}\boldsymbol{c}\boldsymbol{t}\boldsymbol{l}\boldsymbol{y}\;\boldsymbol{s}\boldsymbol{o}\boldsymbol{l}\boldsymbol{v}\boldsymbol{e}\boldsymbol{d} | \sim {\mathcal{F}}_{\boldsymbol{N}\boldsymbol{B}}\left({\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}\right)=\boldsymbol{w}\boldsymbol{r}\boldsymbol{o}\boldsymbol{n}\boldsymbol{g}\boldsymbol{l}\boldsymbol{y}\;\boldsymbol{s}\boldsymbol{o}\boldsymbol{l}\boldsymbol{v}\boldsymbol{e}\boldsymbol{d} |
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | {\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{P}_{AC}} | {\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{N}_{AC}} |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | {\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{P}_{AC}} | {\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{N}_{AC}} |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | {\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}} | {\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{N}_{AC}} |
Note: {\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{P}_{AC}}, {\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{N}_{AC}} = Expenses of right sort and mistake sort of idea ử in agreed judgment; {\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{P}_{AC}}, {\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{N}_{AC}} = \mathrm{E}\mathrm{x}\mathrm{p}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{e}\mathrm{s}\; \mathrm{o}\mathrm{f}\; \mathrm{t}\mathrm{h}\mathrm{e}\; \mathrm{r}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\; \mathrm{s}\mathrm{o}\mathrm{r}\mathrm{t}\; \mathrm{a}\mathrm{n}\mathrm{d}\; \mathrm{m}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{k}\mathrm{e}\; \mathrm{s}\mathrm{o}\mathrm{r}\mathrm{t}\; \mathrm{o}\mathrm{f}\; \mathrm{t}\mathrm{h}\mathrm{e}\; \mathrm{i}\mathrm{d}\mathrm{e}\mathrm{a}\; \mathrm{ử}\; \mathrm{i}\mathrm{n}\; \mathrm{a}\mathrm{b}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{c}\mathrm{e}\; \mathrm{j}\mathrm{u}\mathrm{d}\mathrm{g}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}; {\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}, {\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{N}_{AC}} = \mathrm{E}\mathrm{x}\mathrm{p}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{e}\mathrm{s}\; \mathrm{o}\mathrm{f}\; \mathrm{t}\mathrm{h}\mathrm{e}\; \mathrm{r}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\; \mathrm{s}\mathrm{o}\mathrm{r}\mathrm{t}\; \mathrm{a}\mathrm{n}\mathrm{d}\; \mathrm{m}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{k}\mathrm{e}\; \mathrm{s}\mathrm{o}\mathrm{r}\mathrm{t}\; \mathrm{o}\mathrm{f}\; \mathrm{t}\mathrm{h}\mathrm{e}\; \mathrm{i}\mathrm{d}\mathrm{e}\mathrm{a}\; \mathrm{ử}\; \mathrm{i}\mathrm{n}\; \mathrm{n}\mathrm{o}\mathrm{n}-\mathrm{a}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{e}\mathrm{d}\; \mathrm{j}\mathrm{u}\mathrm{d}\mathrm{g}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}. |
Symbols | {\mathcal{F}}_{\boldsymbol{B}}\left({\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}\right)=\boldsymbol{C}\boldsymbol{o}\boldsymbol{r}\boldsymbol{r}\boldsymbol{e}\boldsymbol{c}\boldsymbol{t}\boldsymbol{l}\boldsymbol{y}\;\boldsymbol{s}\boldsymbol{o}\boldsymbol{l}\boldsymbol{v}\boldsymbol{e}\boldsymbol{d} | \sim {\mathcal{F}}_{\boldsymbol{N}\boldsymbol{B}}\left({\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}\right)=\boldsymbol{w}\boldsymbol{r}\boldsymbol{o}\boldsymbol{n}\boldsymbol{g}\boldsymbol{l}\boldsymbol{y}\;\boldsymbol{s}\boldsymbol{o}\boldsymbol{l}\boldsymbol{v}\boldsymbol{e}\boldsymbol{d} |
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{P}_{AC}}}=\left(\begin{array}{c}\left({s}_{{S}_{LT}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{P}_{AC}}\right)}, {\alpha }_{SC}\right), \\ \left(\begin{array}{c}{\mu }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{P}_{AC}}\right)\\ {e}^{i2\pi \left({\mu }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{P}_{AC}}\right)\right)}, \\ {\eta }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{P}_{AC}}\right)\\ {e}^{i2\pi \left({\eta }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{P}_{AC}}\right)\right)}\end{array}\right)\end{array}\right) | {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}}=\left(\begin{array}{c}\left({s}_{{S}_{LT}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}\right)}, {\alpha }_{SC}\right), \\ \left(\begin{array}{c}{\mu }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}\right)\\ {e}^{i2\pi \left({\mu }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}\right)\right)}, \\ {\eta }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}\right)\\ {e}^{i2\pi \left({\eta }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}\right)\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{P}_{AC}}}=\left(\begin{array}{c}\left({s}_{{S}_{LT}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{P}_{AC}}\right)}, {\alpha }_{SC}\right), \\ \left(\begin{array}{c}{\mu }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{P}_{AC}}\right)\\ {e}^{i2\pi \left({\mu }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{P}_{AC}}\right)\right)}, \\ {\eta }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{P}_{AC}}\right)\\ {e}^{i2\pi \left({\eta }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{P}_{AC}}\right)\right)}\end{array}\right)\end{array}\right) | {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{N}_{AC}}}=\left(\begin{array}{c}\left({s}_{{S}_{LT}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{N}_{AC}}\right)}, {\alpha }_{SC}\right), \\ \left(\begin{array}{c}{\mu }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{N}_{AC}}\right)\\ {e}^{i2\pi \left({\mu }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{N}_{AC}}\right)\right)}, \\ {\eta }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{N}_{AC}}\right)\\ {e}^{i2\pi \left({\eta }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{N}_{AC}}\right)\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}}=\left(\begin{array}{c}\left({s}_{{S}_{LT}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}\right)}, {\alpha }_{SC}\right), \\ \left(\begin{array}{c}{\mu }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}\right)\\ {e}^{i2\pi \left({\mu }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}\right)\right)}, \\ {\eta }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}\right)\\ {e}^{i2\pi \left({\eta }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}\right)\right)}\end{array}\right)\end{array}\right) | {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}}=\left(\begin{array}{c}\left({s}_{{S}_{LT}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{N}_{AC}}\right)}, {\alpha }_{SC}\right), \\ \left(\begin{array}{c}{\mu }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{N}_{AC}}\right)\\ {e}^{i2\pi \left({\mu }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{N}_{AC}}\right)\right)}, \\ {\eta }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{N}_{AC}}\right)\\ {e}^{i2\pi \left({\eta }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{N}_{AC}}\right)\right)}\end{array}\right)\end{array}\right) |
Note: {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{P}_{AC}}}, {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{N}_{AC}}}= \mathrm{E}\mathrm{x}\mathrm{p}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{e}\mathrm{s}\; \mathrm{o}\mathrm{f}\; \mathrm{t}\mathrm{h}\mathrm{e}\; \mathrm{r}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\; \mathrm{s}\mathrm{o}\mathrm{r}\mathrm{t}\; \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{m}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{k}\mathrm{e}\; \mathrm{s}\mathrm{o}\mathrm{r}\mathrm{t}\; \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e}\; \mathrm{i}\mathrm{d}\mathrm{e}\mathrm{a}\mathrm{ử}\mathrm{i}\mathrm{n}\; \mathrm{a}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{e}\mathrm{d}\; \mathrm{j}\mathrm{u}\mathrm{d}\mathrm{g}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}; {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{P}_{AC}}}, {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{N}_{AC}}}=\; \mathrm{E}\mathrm{x}\mathrm{p}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{e}\mathrm{s}\; \mathrm{o}\mathrm{f}\; \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{r}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\; \mathrm{s}\mathrm{o}\mathrm{r}\mathrm{t}\; \mathrm{a}\mathrm{n}\mathrm{d}\; \mathrm{m}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{k}\mathrm{e}\; \mathrm{s}\mathrm{o}\mathrm{r}\mathrm{t}\; \mathrm{o}\mathrm{f}\; \mathrm{t}\mathrm{h}\mathrm{e}\; \mathrm{i}\mathrm{d}\mathrm{e}\mathrm{a}\mathrm{ử}\mathrm{i}\mathrm{n} \mathrm{a}\mathrm{b}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}\; \mathrm{j}\mathrm{u}\mathrm{d}\mathrm{g}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}; {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}}, {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{N}_{AC}}}= \mathrm{E}\mathrm{x}\mathrm{p}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{e}\mathrm{s}\; \mathrm{o}\mathrm{f}\; \mathrm{t}\mathrm{h}\mathrm{e}\; \mathrm{r}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\; \mathrm{s}\mathrm{o}\mathrm{r}\mathrm{t}\; \mathrm{a}\mathrm{n}\mathrm{d}\; \mathrm{m}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{k}\mathrm{e} \mathrm{s}\mathrm{o}\mathrm{r}\mathrm{t}\; \mathrm{o}\mathrm{f}\; \mathrm{t}\mathrm{h}\mathrm{e}\; \mathrm{i}\mathrm{d}\mathrm{e}\mathrm{a}\mathrm{ử}\mathrm{i}\mathrm{n}\; \mathrm{n}\mathrm{o}\mathrm{n}-\mathrm{a}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{e}\mathrm{d}\; \mathrm{j}\mathrm{u}\mathrm{d}\mathrm{g}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}. |
{\mathrm{ử}}_{1} | {\mathrm{ử}}_{2} | |||
{\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | {\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | |
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{1}, 0.01\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.02\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.03\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.04\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{3}, 0.011\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.021\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{5}, 0.031\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.041\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{4}, 0.012\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}\\, 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.022\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.032\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.042\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) |
{\mathrm{ử}}_{3} | {\mathrm{ử}}_{4} | |||
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.013\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.023\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.033\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.04\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{2}, 0.014\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.024\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.034\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.043\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{3}, 0.015\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.025\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{3}, 0.035\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.044\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) |
{\bf{ử}}_{1} | {\bf{ử}}_{2} | |||
{\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | {\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | |
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.02\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.03\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.04\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{5}, 0.05\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{1}, 0.021\right), \\ \left(\begin{array}{c}0.81{e}^{i2\pi \left(0.81\right)}, \\ 0.11{e}^{i2\pi \left(0.11\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{3}, 0.031\right), \\ \left(\begin{array}{c}0.61{e}^{i2\pi \left(0.61\right)}, \\ 0.21{e}^{i2\pi \left(0.21\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.041\right), \\ \left(\begin{array}{c}0.1{e}^{i2\pi \left(0.1\right)}, \\ 0.41{e}^{i2\pi \left(0.41\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.01\right), \\ \left(\begin{array}{c}0.71{e}^{i2\pi \left(0.71\right)}, \\ 0.21{e}^{i2\pi \left(0.21\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{2}, 0.022\right), \\ \left(\begin{array}{c}0.82{e}^{i2\pi \left(0.82\right)}, \\ 0.12{e}^{i2\pi \left(0.12\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.032\right), \\ \left(\begin{array}{c}0.62{e}^{i2\pi \left(0.62\right)}, \\ 0.22{e}^{i2\pi \left(0.22\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.042\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.042\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) |
{\bf{ử}}_{3} | {\bf{ử}}_{4} | |||
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.03\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.04\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.03\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.04\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{5}, 0.031\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.041\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{3}, 0.031\right), \\ \left(\begin{array}{c}0.61{e}^{i2\pi \left(0.61\right)}, \\ 0.21{e}^{i2\pi \left(0.21\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.041\right), \\ \left(\begin{array}{c}0.1{e}^{i2\pi \left(0.1\right)}, \\ 0.41{e}^{i2\pi \left(0.41\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{4}, 0.032\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.042\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.032\right), \\ \left(\begin{array}{c}0.62{e}^{i2\pi \left(0.62\right)}, \\ 0.22{e}^{i2\pi \left(0.22\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.042\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) |
{\bf{ử}}_{1} | {\bf{ử}}_{2} | |||
{\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | {\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | |
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.013\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.023\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.033\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.04\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{2}, 0.014\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.024\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.034\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.043\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.03\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.04\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.03\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.04\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) |
{\bf{ử}}_{3} | {\bf{ử}}_{4} | |||
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.013\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.023\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.033\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.04\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.02\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.03\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.04\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{5}, 0.05\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{1}, 0.021\right), \\ \left(\begin{array}{c}0.81{e}^{i2\pi \left(0.81\right)}, \\ 0.11{e}^{i2\pi \left(0.11\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{3}, 0.031\right), \\ \left(\begin{array}{c}0.61{e}^{i2\pi \left(0.61\right)}, \\ 0.21{e}^{i2\pi \left(0.21\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.041\right), \\ \left(\begin{array}{c}0.1{e}^{i2\pi \left(0.1\right)}, \\ 0.41{e}^{i2\pi \left(0.41\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.01\right), \\ \left(\begin{array}{c}0.71{e}^{i2\pi \left(0.71\right)}, \\ 0.21{e}^{i2\pi \left(0.21\right)}\end{array}\right)\end{array}\right) |
{\bf{ử}}_{1} | {\bf{ử}}_{2} | |||
{\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | {\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | |
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.012\right), \\ \left(\begin{array}{c}0.299{e}^{i2\pi \left(0.299\right)}, \\ 0.678{e}^{i2\pi \left(0.678\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1.41}, 0.021\right), \\ \left(\begin{array}{c}0.275{e}^{i2\pi \left(0.275\right)}, \\ 0.675{e}^{i2\pi \left(0.675\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.031\right), \\ \left(\begin{array}{c}0.251{e}^{i2\pi \left(0.251\right)}, \\ 0.622{e}^{i2\pi \left(0.622\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1.39}, 0.042\right), \\ \left(\begin{array}{c}0.274{e}^{i2\pi \left(0.274\right)}, \\ 0.66{e}^{i2\pi \left(0.66\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0.72}, 0.0112\right), \\ \left(\begin{array}{c}0.293{e}^{i2\pi \left(0.293\right)}, \\ 0.632{e}^{i2\pi \left(0.632\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.76}, 0.022\right), \\ \left(\begin{array}{c}0.274{e}^{i2\pi \left(0.274\right)}, \\ 0.606{e}^{i2\pi \left(0.606\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.85}, 0.033\right), \\ \left(\begin{array}{c}0.274{e}^{i2\pi \left(0.274\right)}, \\ 0.656{e}^{i2\pi \left(0.656\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.74}, 0.043\right), \\ \left(\begin{array}{c}0.269{e}^{i2\pi \left(0.269\right)}, \\ 0.659{e}^{i2\pi \left(0.659\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{1.04}, 0.013\right), \\ \left(\begin{array}{c}0.34{e}^{i2\pi \left(0.34\right)}, \\ 0.599{e}^{i2\pi \left(0.599\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.18}, 0.024\right), \\ \left(\begin{array}{c}0.318{e}^{i2\pi \left(0.318\right)}, \\ 0.563{e}^{i2\pi \left(0.563\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1.41}, 0.032\right), \\ \left(\begin{array}{c}0.297{e}^{i2\pi \left(0.297\right)}, \\ 0.657{e}^{i2\pi \left(0.657\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.14}, 0.042\right), \\ \left(\begin{array}{c}0.318{e}^{i2\pi \left(0.318\right)}, \\ 0.619{e}^{i2\pi \left(0.619\right)}\end{array}\right)\end{array}\right) |
{\mathrm{ử}}_{3} | {\mathrm{ử}}_{4} | |||
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.0142\right), \\ \left(\begin{array}{c}0.279{e}^{i2\pi \left(0.279\right)}, \\ 0.56{e}^{i2\pi \left(0.56\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1.443}, 0.0221\right), \\ \left(\begin{array}{c}0.25{e}^{i2\pi \left(0.25\right)}, \\ 0.75{e}^{i2\pi \left(0.75\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.0321\right), \\ \left(\begin{array}{c}0.21{e}^{i2\pi \left(0.21\right)}, \\ 0.62{e}^{i2\pi \left(0.62\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1.59}, 0.043\right), \\ \left(\begin{array}{c}0.254{e}^{i2\pi \left(0.254\right)}, \\ 0.70{e}^{i2\pi \left(0.70\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0.69}, 0.013\right), \\ \left(\begin{array}{c}0.288{e}^{i2\pi \left(0.288\right)}, \\ 0.612{e}^{i2\pi \left(0.612\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.81}, 0.023\right), \\ \left(\begin{array}{c}0.287{e}^{i2\pi \left(0.287\right)}, \\ 0.599{e}^{i2\pi \left(0.599\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.81}, 0.032\right), \\ \left(\begin{array}{c}0.257{e}^{i2\pi \left(0.257\right)}, \\ 0.670{e}^{i2\pi \left(0.670\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.57}, 0.0434\right), \\ \left(\begin{array}{c}0.273{e}^{i2\pi \left(0.273\right)}, \\ 0.69{e}^{i2\pi \left(0.69\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{1.31}, 0.023\right), \\ \left(\begin{array}{c}0.349{e}^{i2\pi \left(0.349\right)}, \\ 0.615{e}^{i2\pi \left(0.615\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.78}, 0.029\right), \\ \left(\begin{array}{c}0.389{e}^{i2\pi \left(0.389\right)}, \\ 0.569{e}^{i2\pi \left(0.569\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1.84}, 0.038\right), \\ \left(\begin{array}{c}0.302{e}^{i2\pi \left(0.302\right)}, \\ 0.686{e}^{i2\pi \left(0.686\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.35}, 0.0423\right), \\ \left(\begin{array}{c}0.319{e}^{i2\pi \left(0.319\right)}, \\ 0.617{e}^{i2\pi \left(0.617\right)}\end{array}\right)\end{array}\right) |
Symbols | {\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right) | {\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right) | {\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right) |
{\boldsymbol{ử}}_{1} | \left(\begin{array}{c}\left({s}_{0}, 0.1866\right), \\ \left(\begin{array}{c}0.2504{e}^{i2\pi \left(0.2504\right)}, \\ 0.6762{e}^{i2\pi \left(0.6762\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.1656\right), \\ \left(\begin{array}{c}0.2817{e}^{i2\pi \left(0.2817\right)}, \\ 0.6163{e}^{i2\pi \left(0.6163\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.1244\right), \\ \left(\begin{array}{c}0.3269{e}^{i2\pi \left(0.3269\right)}, \\ 0.5771{e}^{i2\pi \left(0.5771\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{ử}}_{2} | \left(\begin{array}{c}\left({s}_{1}, 0.0044\right), \\ \left(\begin{array}{c}0.2649{e}^{i2\pi \left(0.2649\right)}, \\ 0.6445{e}^{i2\pi \left(0.6445\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.1346\right), \\ \left(\begin{array}{c}0.271{e}^{i2\pi \left(0.271\right)}, \\ 0.6578{e}^{i2\pi \left(0.6578\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.1676\right), \\ \left(\begin{array}{c}0.3097{e}^{i2\pi \left(0.3097\right)}, \\ 0.6339{e}^{i2\pi \left(0.6339\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{ử}}_{3} | \left(\begin{array}{c}\left({s}_{0}, 0.1921\right), \\ \left(\begin{array}{c}0.2617{e}^{i2\pi \left(0.2617\right)}, \\ 0.6673{e}^{i2\pi \left(0.6673\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.1714\right), \\ \left(\begin{array}{c}0.2874{e}^{i2\pi \left(0.2874\right)}, \\ 0.6042{e}^{i2\pi \left(0.6042\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.025\right), \\ \left(\begin{array}{c}0.3733{e}^{i2\pi \left(0.3733\right)}, \\ 0.587{e}^{i2\pi \left(0.587\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{ử}}_{4} | \left(\begin{array}{c}\left({s}_{1}, 0.0166\right), \\ \left(\begin{array}{c}0.2367{e}^{i2\pi \left(0.2367\right)}, \\ 0.6668{e}^{i2\pi \left(0.6668\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.172\right), \\ \left(\begin{array}{c}0.2666{e}^{i2\pi \left(0.2666\right)}, \\ 0.6819{e}^{i2\pi \left(0.6819\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.192\right), \\ \left(\begin{array}{c}0.3123{e}^{i2\pi \left(0.3123\right)}, \\ 0.6437{e}^{i2\pi \left(0.6437\right)}\end{array}\right)\end{array}\right) |
Symbols | {\boldsymbol{Q}}_{\boldsymbol{E}\boldsymbol{V}}\left({\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right)\right) | {\boldsymbol{Q}}_{\boldsymbol{E}\boldsymbol{V}}\left({\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right)\right) | {\boldsymbol{Q}}_{\boldsymbol{E}\boldsymbol{V}}\left({\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right)\right) |
{\boldsymbol{ử}}_{1} | 0.0137 | 0.017 | 0.0119 |
{\boldsymbol{ử}}_{2} | 0.0185 | 0.0096 | 0.0095 |
{\boldsymbol{ử}}_{3} | 0.0136 | 0.0186 | 0.0089 |
{\boldsymbol{ử}}_{4} | 0.0211 | 0.0088 | 0.0085 |
Symbols | {\boldsymbol{G}}_{\boldsymbol{A}\boldsymbol{F}}\left({\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right)\right) | {\boldsymbol{G}}_{\boldsymbol{A}\boldsymbol{F}}\left({\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right)\right) | {\boldsymbol{G}}_{\boldsymbol{A}\boldsymbol{F}}\left({\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right)\right) |
{\boldsymbol{ử}}_{1} | 0.266 | 0.2222 | 0.1555 |
{\boldsymbol{ử}}_{2} | 0.282 | 0.1867 | 0.2219 |
{\boldsymbol{ử}}_{3} | 0.27 | 0.2257 | 0.2731 |
{\boldsymbol{ử}}_{4} | 0.3127 | 0.2435 | 0.2656 |
Enterprises | Decision rule |
{\boldsymbol{ử}}_{1} | {P}_{AC-1} |
{\boldsymbol{ử}}_{2} | {P}_{AC-1} |
{\boldsymbol{ử}}_{3} | {P}_{AC-1} |
{\boldsymbol{ử}}_{4} | {P}_{AC-1} |
Enterprises | {\boldsymbol{ử}}_{1} | {\boldsymbol{ử}}_{2} | {\boldsymbol{ử}}_{3} | {\boldsymbol{ử}}_{4} |
Proposed work for q=1 | {P}_{AC-1} | {P}_{AC-1} | {P}_{AC-1} | {P}_{AC-1} |
Proposed work for q=2 | {P}_{AC-1} | {P}_{AC-1} | {P}_{AC-1} | {P}_{AC-1} |
Proposed work for q=3 | {P}_{AC-1} | {P}_{AC-1} | {P}_{AC-1} | {P}_{AC-1} |
Symbols | {\mathcal{F}}_{\boldsymbol{B}}\left({\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}\right)=\boldsymbol{C}\boldsymbol{o}\boldsymbol{r}\boldsymbol{r}\boldsymbol{e}\boldsymbol{c}\boldsymbol{t}\boldsymbol{l}\boldsymbol{y}\;\boldsymbol{s}\boldsymbol{o}\boldsymbol{l}\boldsymbol{v}\boldsymbol{e}\boldsymbol{d} | \sim {\mathcal{F}}_{\boldsymbol{N}\boldsymbol{B}}\left({\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}\right)=\boldsymbol{w}\boldsymbol{r}\boldsymbol{o}\boldsymbol{n}\boldsymbol{g}\boldsymbol{l}\boldsymbol{y}\;\boldsymbol{s}\boldsymbol{o}\boldsymbol{l}\boldsymbol{v}\boldsymbol{e}\boldsymbol{d} |
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | {\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{P}_{AC}} | {\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{N}_{AC}} |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | {\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{P}_{AC}} | {\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{N}_{AC}} |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | {\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}} | {\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{N}_{AC}} |
Note: {\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{P}_{AC}}, {\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{N}_{AC}} = Expenses of right sort and mistake sort of idea ử in agreed judgment; {\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{P}_{AC}}, {\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{N}_{AC}} = \mathrm{E}\mathrm{x}\mathrm{p}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{e}\mathrm{s}\; \mathrm{o}\mathrm{f}\; \mathrm{t}\mathrm{h}\mathrm{e}\; \mathrm{r}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\; \mathrm{s}\mathrm{o}\mathrm{r}\mathrm{t}\; \mathrm{a}\mathrm{n}\mathrm{d}\; \mathrm{m}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{k}\mathrm{e}\; \mathrm{s}\mathrm{o}\mathrm{r}\mathrm{t}\; \mathrm{o}\mathrm{f}\; \mathrm{t}\mathrm{h}\mathrm{e}\; \mathrm{i}\mathrm{d}\mathrm{e}\mathrm{a}\; \mathrm{ử}\; \mathrm{i}\mathrm{n}\; \mathrm{a}\mathrm{b}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{c}\mathrm{e}\; \mathrm{j}\mathrm{u}\mathrm{d}\mathrm{g}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}; {\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}, {\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{N}_{AC}} = \mathrm{E}\mathrm{x}\mathrm{p}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{e}\mathrm{s}\; \mathrm{o}\mathrm{f}\; \mathrm{t}\mathrm{h}\mathrm{e}\; \mathrm{r}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\; \mathrm{s}\mathrm{o}\mathrm{r}\mathrm{t}\; \mathrm{a}\mathrm{n}\mathrm{d}\; \mathrm{m}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{k}\mathrm{e}\; \mathrm{s}\mathrm{o}\mathrm{r}\mathrm{t}\; \mathrm{o}\mathrm{f}\; \mathrm{t}\mathrm{h}\mathrm{e}\; \mathrm{i}\mathrm{d}\mathrm{e}\mathrm{a}\; \mathrm{ử}\; \mathrm{i}\mathrm{n}\; \mathrm{n}\mathrm{o}\mathrm{n}-\mathrm{a}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{e}\mathrm{d}\; \mathrm{j}\mathrm{u}\mathrm{d}\mathrm{g}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}. |
Symbols | {\mathcal{F}}_{\boldsymbol{B}}\left({\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}\right)=\boldsymbol{C}\boldsymbol{o}\boldsymbol{r}\boldsymbol{r}\boldsymbol{e}\boldsymbol{c}\boldsymbol{t}\boldsymbol{l}\boldsymbol{y}\;\boldsymbol{s}\boldsymbol{o}\boldsymbol{l}\boldsymbol{v}\boldsymbol{e}\boldsymbol{d} | \sim {\mathcal{F}}_{\boldsymbol{N}\boldsymbol{B}}\left({\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}\right)=\boldsymbol{w}\boldsymbol{r}\boldsymbol{o}\boldsymbol{n}\boldsymbol{g}\boldsymbol{l}\boldsymbol{y}\;\boldsymbol{s}\boldsymbol{o}\boldsymbol{l}\boldsymbol{v}\boldsymbol{e}\boldsymbol{d} |
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{P}_{AC}}}=\left(\begin{array}{c}\left({s}_{{S}_{LT}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{P}_{AC}}\right)}, {\alpha }_{SC}\right), \\ \left(\begin{array}{c}{\mu }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{P}_{AC}}\right)\\ {e}^{i2\pi \left({\mu }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{P}_{AC}}\right)\right)}, \\ {\eta }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{P}_{AC}}\right)\\ {e}^{i2\pi \left({\eta }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{P}_{AC}}\right)\right)}\end{array}\right)\end{array}\right) | {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}}=\left(\begin{array}{c}\left({s}_{{S}_{LT}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}\right)}, {\alpha }_{SC}\right), \\ \left(\begin{array}{c}{\mu }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}\right)\\ {e}^{i2\pi \left({\mu }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}\right)\right)}, \\ {\eta }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}\right)\\ {e}^{i2\pi \left({\eta }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}\right)\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{P}_{AC}}}=\left(\begin{array}{c}\left({s}_{{S}_{LT}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{P}_{AC}}\right)}, {\alpha }_{SC}\right), \\ \left(\begin{array}{c}{\mu }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{P}_{AC}}\right)\\ {e}^{i2\pi \left({\mu }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{P}_{AC}}\right)\right)}, \\ {\eta }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{P}_{AC}}\right)\\ {e}^{i2\pi \left({\eta }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{P}_{AC}}\right)\right)}\end{array}\right)\end{array}\right) | {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{N}_{AC}}}=\left(\begin{array}{c}\left({s}_{{S}_{LT}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{N}_{AC}}\right)}, {\alpha }_{SC}\right), \\ \left(\begin{array}{c}{\mu }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{N}_{AC}}\right)\\ {e}^{i2\pi \left({\mu }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{N}_{AC}}\right)\right)}, \\ {\eta }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{N}_{AC}}\right)\\ {e}^{i2\pi \left({\eta }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{N}_{AC}}\right)\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}}=\left(\begin{array}{c}\left({s}_{{S}_{LT}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}\right)}, {\alpha }_{SC}\right), \\ \left(\begin{array}{c}{\mu }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}\right)\\ {e}^{i2\pi \left({\mu }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}\right)\right)}, \\ {\eta }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}\right)\\ {e}^{i2\pi \left({\eta }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}\right)\right)}\end{array}\right)\end{array}\right) | {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}}=\left(\begin{array}{c}\left({s}_{{S}_{LT}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{N}_{AC}}\right)}, {\alpha }_{SC}\right), \\ \left(\begin{array}{c}{\mu }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{N}_{AC}}\right)\\ {e}^{i2\pi \left({\mu }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{N}_{AC}}\right)\right)}, \\ {\eta }_{{\mathcal{Q}}_{CQTLRP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{N}_{AC}}\right)\\ {e}^{i2\pi \left({\eta }_{{\mathcal{Q}}_{CQTLIP}}\left({\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{N}_{AC}}\right)\right)}\end{array}\right)\end{array}\right) |
Note: {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{P}_{AC}}}, {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{P}_{AC}{N}_{AC}}}= \mathrm{E}\mathrm{x}\mathrm{p}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{e}\mathrm{s}\; \mathrm{o}\mathrm{f}\; \mathrm{t}\mathrm{h}\mathrm{e}\; \mathrm{r}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\; \mathrm{s}\mathrm{o}\mathrm{r}\mathrm{t}\; \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{m}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{k}\mathrm{e}\; \mathrm{s}\mathrm{o}\mathrm{r}\mathrm{t}\; \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e}\; \mathrm{i}\mathrm{d}\mathrm{e}\mathrm{a}\mathrm{ử}\mathrm{i}\mathrm{n}\; \mathrm{a}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{e}\mathrm{d}\; \mathrm{j}\mathrm{u}\mathrm{d}\mathrm{g}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}; {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{P}_{AC}}}, {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{B}_{AC}{N}_{AC}}}=\; \mathrm{E}\mathrm{x}\mathrm{p}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{e}\mathrm{s}\; \mathrm{o}\mathrm{f}\; \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{r}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\; \mathrm{s}\mathrm{o}\mathrm{r}\mathrm{t}\; \mathrm{a}\mathrm{n}\mathrm{d}\; \mathrm{m}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{k}\mathrm{e}\; \mathrm{s}\mathrm{o}\mathrm{r}\mathrm{t}\; \mathrm{o}\mathrm{f}\; \mathrm{t}\mathrm{h}\mathrm{e}\; \mathrm{i}\mathrm{d}\mathrm{e}\mathrm{a}\mathrm{ử}\mathrm{i}\mathrm{n} \mathrm{a}\mathrm{b}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}\; \mathrm{j}\mathrm{u}\mathrm{d}\mathrm{g}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}; {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{P}_{AC}}}, {\mathcal{Q}}_{CQTL-{\stackrel{-}{\mathcal{Q}}}_{CQ-{N}_{AC}{N}_{AC}}}= \mathrm{E}\mathrm{x}\mathrm{p}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{e}\mathrm{s}\; \mathrm{o}\mathrm{f}\; \mathrm{t}\mathrm{h}\mathrm{e}\; \mathrm{r}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\; \mathrm{s}\mathrm{o}\mathrm{r}\mathrm{t}\; \mathrm{a}\mathrm{n}\mathrm{d}\; \mathrm{m}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{k}\mathrm{e} \mathrm{s}\mathrm{o}\mathrm{r}\mathrm{t}\; \mathrm{o}\mathrm{f}\; \mathrm{t}\mathrm{h}\mathrm{e}\; \mathrm{i}\mathrm{d}\mathrm{e}\mathrm{a}\mathrm{ử}\mathrm{i}\mathrm{n}\; \mathrm{n}\mathrm{o}\mathrm{n}-\mathrm{a}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{e}\mathrm{d}\; \mathrm{j}\mathrm{u}\mathrm{d}\mathrm{g}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}. |
{\mathrm{ử}}_{1} | {\mathrm{ử}}_{2} | |||
{\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | {\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | |
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{1}, 0.01\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.02\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.03\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.04\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{3}, 0.011\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.021\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{5}, 0.031\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.041\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{4}, 0.012\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}\\, 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.022\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.032\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.042\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) |
{\mathrm{ử}}_{3} | {\mathrm{ử}}_{4} | |||
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.013\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.023\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.033\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.04\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{2}, 0.014\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.024\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.034\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.043\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{3}, 0.015\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.025\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{3}, 0.035\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.044\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) |
{\bf{ử}}_{1} | {\bf{ử}}_{2} | |||
{\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | {\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | |
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.02\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.03\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.04\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{5}, 0.05\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{1}, 0.021\right), \\ \left(\begin{array}{c}0.81{e}^{i2\pi \left(0.81\right)}, \\ 0.11{e}^{i2\pi \left(0.11\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{3}, 0.031\right), \\ \left(\begin{array}{c}0.61{e}^{i2\pi \left(0.61\right)}, \\ 0.21{e}^{i2\pi \left(0.21\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.041\right), \\ \left(\begin{array}{c}0.1{e}^{i2\pi \left(0.1\right)}, \\ 0.41{e}^{i2\pi \left(0.41\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.01\right), \\ \left(\begin{array}{c}0.71{e}^{i2\pi \left(0.71\right)}, \\ 0.21{e}^{i2\pi \left(0.21\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{2}, 0.022\right), \\ \left(\begin{array}{c}0.82{e}^{i2\pi \left(0.82\right)}, \\ 0.12{e}^{i2\pi \left(0.12\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.032\right), \\ \left(\begin{array}{c}0.62{e}^{i2\pi \left(0.62\right)}, \\ 0.22{e}^{i2\pi \left(0.22\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.042\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.042\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) |
{\bf{ử}}_{3} | {\bf{ử}}_{4} | |||
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.03\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.04\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.03\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.04\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{5}, 0.031\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.041\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{3}, 0.031\right), \\ \left(\begin{array}{c}0.61{e}^{i2\pi \left(0.61\right)}, \\ 0.21{e}^{i2\pi \left(0.21\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.041\right), \\ \left(\begin{array}{c}0.1{e}^{i2\pi \left(0.1\right)}, \\ 0.41{e}^{i2\pi \left(0.41\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{4}, 0.032\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.042\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.032\right), \\ \left(\begin{array}{c}0.62{e}^{i2\pi \left(0.62\right)}, \\ 0.22{e}^{i2\pi \left(0.22\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.042\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) |
{\bf{ử}}_{1} | {\bf{ử}}_{2} | |||
{\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | {\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | |
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.013\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.023\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.033\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.04\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{2}, 0.014\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.024\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.034\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{2}, 0.043\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.03\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.04\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.03\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.04\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) |
{\bf{ử}}_{3} | {\bf{ử}}_{4} | |||
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.013\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.023\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.033\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.04\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.02\right), \\ \left(\begin{array}{c}0.8{e}^{i2\pi \left(0.8\right)}, \\ 0.1{e}^{i2\pi \left(0.1\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.03\right), \\ \left(\begin{array}{c}0.6{e}^{i2\pi \left(0.6\right)}, \\ 0.2{e}^{i2\pi \left(0.2\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.04\right), \\ \left(\begin{array}{c}0.5{e}^{i2\pi \left(0.5\right)}, \\ 0.4{e}^{i2\pi \left(0.4\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{5}, 0.05\right), \\ \left(\begin{array}{c}0.7{e}^{i2\pi \left(0.7\right)}, \\ 0.3{e}^{i2\pi \left(0.3\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{1}, 0.021\right), \\ \left(\begin{array}{c}0.81{e}^{i2\pi \left(0.81\right)}, \\ 0.11{e}^{i2\pi \left(0.11\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{3}, 0.031\right), \\ \left(\begin{array}{c}0.61{e}^{i2\pi \left(0.61\right)}, \\ 0.21{e}^{i2\pi \left(0.21\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.041\right), \\ \left(\begin{array}{c}0.1{e}^{i2\pi \left(0.1\right)}, \\ 0.41{e}^{i2\pi \left(0.41\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{4}, 0.01\right), \\ \left(\begin{array}{c}0.71{e}^{i2\pi \left(0.71\right)}, \\ 0.21{e}^{i2\pi \left(0.21\right)}\end{array}\right)\end{array}\right) |
{\bf{ử}}_{1} | {\bf{ử}}_{2} | |||
{\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | {\mathcal{F}}_{B} | {\sim \mathcal{F}}_{NB} | |
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.012\right), \\ \left(\begin{array}{c}0.299{e}^{i2\pi \left(0.299\right)}, \\ 0.678{e}^{i2\pi \left(0.678\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1.41}, 0.021\right), \\ \left(\begin{array}{c}0.275{e}^{i2\pi \left(0.275\right)}, \\ 0.675{e}^{i2\pi \left(0.675\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.031\right), \\ \left(\begin{array}{c}0.251{e}^{i2\pi \left(0.251\right)}, \\ 0.622{e}^{i2\pi \left(0.622\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1.39}, 0.042\right), \\ \left(\begin{array}{c}0.274{e}^{i2\pi \left(0.274\right)}, \\ 0.66{e}^{i2\pi \left(0.66\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0.72}, 0.0112\right), \\ \left(\begin{array}{c}0.293{e}^{i2\pi \left(0.293\right)}, \\ 0.632{e}^{i2\pi \left(0.632\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.76}, 0.022\right), \\ \left(\begin{array}{c}0.274{e}^{i2\pi \left(0.274\right)}, \\ 0.606{e}^{i2\pi \left(0.606\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.85}, 0.033\right), \\ \left(\begin{array}{c}0.274{e}^{i2\pi \left(0.274\right)}, \\ 0.656{e}^{i2\pi \left(0.656\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.74}, 0.043\right), \\ \left(\begin{array}{c}0.269{e}^{i2\pi \left(0.269\right)}, \\ 0.659{e}^{i2\pi \left(0.659\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{1.04}, 0.013\right), \\ \left(\begin{array}{c}0.34{e}^{i2\pi \left(0.34\right)}, \\ 0.599{e}^{i2\pi \left(0.599\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.18}, 0.024\right), \\ \left(\begin{array}{c}0.318{e}^{i2\pi \left(0.318\right)}, \\ 0.563{e}^{i2\pi \left(0.563\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1.41}, 0.032\right), \\ \left(\begin{array}{c}0.297{e}^{i2\pi \left(0.297\right)}, \\ 0.657{e}^{i2\pi \left(0.657\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.14}, 0.042\right), \\ \left(\begin{array}{c}0.318{e}^{i2\pi \left(0.318\right)}, \\ 0.619{e}^{i2\pi \left(0.619\right)}\end{array}\right)\end{array}\right) |
{\mathrm{ử}}_{3} | {\mathrm{ử}}_{4} | |||
{\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0}, 0.0142\right), \\ \left(\begin{array}{c}0.279{e}^{i2\pi \left(0.279\right)}, \\ 0.56{e}^{i2\pi \left(0.56\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1.443}, 0.0221\right), \\ \left(\begin{array}{c}0.25{e}^{i2\pi \left(0.25\right)}, \\ 0.75{e}^{i2\pi \left(0.75\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.0321\right), \\ \left(\begin{array}{c}0.21{e}^{i2\pi \left(0.21\right)}, \\ 0.62{e}^{i2\pi \left(0.62\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1.59}, 0.043\right), \\ \left(\begin{array}{c}0.254{e}^{i2\pi \left(0.254\right)}, \\ 0.70{e}^{i2\pi \left(0.70\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{0.69}, 0.013\right), \\ \left(\begin{array}{c}0.288{e}^{i2\pi \left(0.288\right)}, \\ 0.612{e}^{i2\pi \left(0.612\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.81}, 0.023\right), \\ \left(\begin{array}{c}0.287{e}^{i2\pi \left(0.287\right)}, \\ 0.599{e}^{i2\pi \left(0.599\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.81}, 0.032\right), \\ \left(\begin{array}{c}0.257{e}^{i2\pi \left(0.257\right)}, \\ 0.670{e}^{i2\pi \left(0.670\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.57}, 0.0434\right), \\ \left(\begin{array}{c}0.273{e}^{i2\pi \left(0.273\right)}, \\ 0.69{e}^{i2\pi \left(0.69\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}} | \left(\begin{array}{c}\left({s}_{1.31}, 0.023\right), \\ \left(\begin{array}{c}0.349{e}^{i2\pi \left(0.349\right)}, \\ 0.615{e}^{i2\pi \left(0.615\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.78}, 0.029\right), \\ \left(\begin{array}{c}0.389{e}^{i2\pi \left(0.389\right)}, \\ 0.569{e}^{i2\pi \left(0.569\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1.84}, 0.038\right), \\ \left(\begin{array}{c}0.302{e}^{i2\pi \left(0.302\right)}, \\ 0.686{e}^{i2\pi \left(0.686\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0.35}, 0.0423\right), \\ \left(\begin{array}{c}0.319{e}^{i2\pi \left(0.319\right)}, \\ 0.617{e}^{i2\pi \left(0.617\right)}\end{array}\right)\end{array}\right) |
Symbols | {\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right) | {\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right) | {\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right) |
{\boldsymbol{ử}}_{1} | \left(\begin{array}{c}\left({s}_{0}, 0.1866\right), \\ \left(\begin{array}{c}0.2504{e}^{i2\pi \left(0.2504\right)}, \\ 0.6762{e}^{i2\pi \left(0.6762\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.1656\right), \\ \left(\begin{array}{c}0.2817{e}^{i2\pi \left(0.2817\right)}, \\ 0.6163{e}^{i2\pi \left(0.6163\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.1244\right), \\ \left(\begin{array}{c}0.3269{e}^{i2\pi \left(0.3269\right)}, \\ 0.5771{e}^{i2\pi \left(0.5771\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{ử}}_{2} | \left(\begin{array}{c}\left({s}_{1}, 0.0044\right), \\ \left(\begin{array}{c}0.2649{e}^{i2\pi \left(0.2649\right)}, \\ 0.6445{e}^{i2\pi \left(0.6445\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.1346\right), \\ \left(\begin{array}{c}0.271{e}^{i2\pi \left(0.271\right)}, \\ 0.6578{e}^{i2\pi \left(0.6578\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.1676\right), \\ \left(\begin{array}{c}0.3097{e}^{i2\pi \left(0.3097\right)}, \\ 0.6339{e}^{i2\pi \left(0.6339\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{ử}}_{3} | \left(\begin{array}{c}\left({s}_{0}, 0.1921\right), \\ \left(\begin{array}{c}0.2617{e}^{i2\pi \left(0.2617\right)}, \\ 0.6673{e}^{i2\pi \left(0.6673\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.1714\right), \\ \left(\begin{array}{c}0.2874{e}^{i2\pi \left(0.2874\right)}, \\ 0.6042{e}^{i2\pi \left(0.6042\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{1}, 0.025\right), \\ \left(\begin{array}{c}0.3733{e}^{i2\pi \left(0.3733\right)}, \\ 0.587{e}^{i2\pi \left(0.587\right)}\end{array}\right)\end{array}\right) |
{\boldsymbol{ử}}_{4} | \left(\begin{array}{c}\left({s}_{1}, 0.0166\right), \\ \left(\begin{array}{c}0.2367{e}^{i2\pi \left(0.2367\right)}, \\ 0.6668{e}^{i2\pi \left(0.6668\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.172\right), \\ \left(\begin{array}{c}0.2666{e}^{i2\pi \left(0.2666\right)}, \\ 0.6819{e}^{i2\pi \left(0.6819\right)}\end{array}\right)\end{array}\right) | \left(\begin{array}{c}\left({s}_{0}, 0.192\right), \\ \left(\begin{array}{c}0.3123{e}^{i2\pi \left(0.3123\right)}, \\ 0.6437{e}^{i2\pi \left(0.6437\right)}\end{array}\right)\end{array}\right) |
Symbols | {\boldsymbol{Q}}_{\boldsymbol{E}\boldsymbol{V}}\left({\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right)\right) | {\boldsymbol{Q}}_{\boldsymbol{E}\boldsymbol{V}}\left({\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right)\right) | {\boldsymbol{Q}}_{\boldsymbol{E}\boldsymbol{V}}\left({\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right)\right) |
{\boldsymbol{ử}}_{1} | 0.0137 | 0.017 | 0.0119 |
{\boldsymbol{ử}}_{2} | 0.0185 | 0.0096 | 0.0095 |
{\boldsymbol{ử}}_{3} | 0.0136 | 0.0186 | 0.0089 |
{\boldsymbol{ử}}_{4} | 0.0211 | 0.0088 | 0.0085 |
Symbols | {\boldsymbol{G}}_{\boldsymbol{A}\boldsymbol{F}}\left({\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{P}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right)\right) | {\boldsymbol{G}}_{\boldsymbol{A}\boldsymbol{F}}\left({\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{B}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right)\right) | {\boldsymbol{G}}_{\boldsymbol{A}\boldsymbol{F}}\left({\boldsymbol{Y}}_{\boldsymbol{E}\boldsymbol{L}}\left({\boldsymbol{\chi }}_{{\boldsymbol{N}}_{\boldsymbol{A}\boldsymbol{C}}}\left|\right[\boldsymbol{ử}]\right)\right) |
{\boldsymbol{ử}}_{1} | 0.266 | 0.2222 | 0.1555 |
{\boldsymbol{ử}}_{2} | 0.282 | 0.1867 | 0.2219 |
{\boldsymbol{ử}}_{3} | 0.27 | 0.2257 | 0.2731 |
{\boldsymbol{ử}}_{4} | 0.3127 | 0.2435 | 0.2656 |
Enterprises | Decision rule |
{\boldsymbol{ử}}_{1} | {P}_{AC-1} |
{\boldsymbol{ử}}_{2} | {P}_{AC-1} |
{\boldsymbol{ử}}_{3} | {P}_{AC-1} |
{\boldsymbol{ử}}_{4} | {P}_{AC-1} |
Enterprises | {\boldsymbol{ử}}_{1} | {\boldsymbol{ử}}_{2} | {\boldsymbol{ử}}_{3} | {\boldsymbol{ử}}_{4} |
Proposed work for q=1 | {P}_{AC-1} | {P}_{AC-1} | {P}_{AC-1} | {P}_{AC-1} |
Proposed work for q=2 | {P}_{AC-1} | {P}_{AC-1} | {P}_{AC-1} | {P}_{AC-1} |
Proposed work for q=3 | {P}_{AC-1} | {P}_{AC-1} | {P}_{AC-1} | {P}_{AC-1} |