Loading [MathJax]/jax/output/SVG/jax.js
Research article Topical Sections

Chronic treatment with escitalopram and venlafaxine affects the neuropeptide S pathway differently in adult Wistar rats exposed to maternal separation

  • Neuropeptide S (NPS), which is a peptide that is involved in the regulation of the stress response, seems to be relevant to the mechanism of action of antidepressants that have anxiolytic properties. However, to date, there have been no reports regarding the effect of long-term treatment with escitalopram or venlafaxine on the NPS system under stress conditions.

    This study aimed to investigate the effects of the above-mentioned antidepressants on the NPS system in adult male Wistar rats that were exposed to neonatal maternal separation (MS).

    Animals were exposed to MS for 360 min. on postnatal days (PNDs) 2–15. MS causes long-lasting behavioral, endocrine and neurochemical consequences that mimic anxiety- and depression-related features. MS and non-stressed rats were given escitalopram or venlafaxine (10mg/kg) IP from PND 69 to 89. The NPS system was analyzed in the brainstem, hypothalamus, amygdala and anterior olfactory nucleus using quantitative RT-PCR and immunohistochemical methods.

    The NPS system was vulnerable to MS in the brainstem and amygdala. In the brainstem, escitalopram down-regulated NPS and NPS mRNA in the MS rats and induced a tendency to reduce the number of NPS-positive cells in the peri-locus coeruleus. In the MS rats, venlafaxine insignificantly decreased the NPSR mRNA levels in the amygdala and a number of NPSR cells in the basolateral amygdala, and increased the NPS mRNA levels in the hypothalamus.

    Our data show that the studied antidepressants affect the NPS system differently and preliminarily suggest that the NPS system might partially mediate the pharmacological effects that are induced by these drugs.

    Citation: Miłosz Gołyszny, Michał Zieliński, Monika Paul-Samojedny, Artur Pałasz, Ewa Obuchowicz. Chronic treatment with escitalopram and venlafaxine affects the neuropeptide S pathway differently in adult Wistar rats exposed to maternal separation[J]. AIMS Neuroscience, 2022, 9(3): 395-422. doi: 10.3934/Neuroscience.2022022

    Related Papers:

    [1] Sohail Ahmad, Ponam Basharat, Saleem Abdullah, Thongchai Botmart, Anuwat Jirawattanapanit . MABAC under non-linear diophantine fuzzy numbers: A new approach for emergency decision support systems. AIMS Mathematics, 2022, 7(10): 17699-17736. doi: 10.3934/math.2022975
    [2] Dongsheng Xu, Xiangxiang Cui, Lijuan Peng, Huaxiang Xian . Distance measures between interval complex neutrosophic sets and their applications in multi-criteria group decision making. AIMS Mathematics, 2020, 5(6): 5700-5715. doi: 10.3934/math.2020365
    [3] Mohammed M. Ali Al-Shamiri, Adeel Farooq, Muhammad Nabeel, Ghous Ali, Dragan Pamučar . Integrating TOPSIS and ELECTRE-Ⅰ methods with cubic m-polar fuzzy sets and its application to the diagnosis of psychiatric disorders. AIMS Mathematics, 2023, 8(5): 11875-11915. doi: 10.3934/math.2023601
    [4] Murugan Palanikumar, Nasreen Kausar, Shams Forruque Ahmed, Seyyed Ahmad Edalatpanah, Ebru Ozbilge, Alper Bulut . New applications of various distance techniques to multi-criteria decision-making challenges for ranking vague sets. AIMS Mathematics, 2023, 8(5): 11397-11424. doi: 10.3934/math.2023577
    [5] Nasser Aedh Alreshidi, Muhammad Rahim, Fazli Amin, Abdulaziz Alenazi . Trapezoidal type-2 Pythagorean fuzzy TODIM approach for sensible decision-making with unknown weights in the presence of hesitancy. AIMS Mathematics, 2023, 8(12): 30462-30486. doi: 10.3934/math.20231556
    [6] Chuan-Yang Ruan, Xiang-Jing Chen, Shi-Cheng Gong, Shahbaz Ali, Bander Almutairi . A decision-making framework based on the Fermatean hesitant fuzzy distance measure and TOPSIS. AIMS Mathematics, 2024, 9(2): 2722-2755. doi: 10.3934/math.2024135
    [7] Jun Hu, Jie Wu, Mengzhe Wang . Research on VIKOR group decision making using WOWA operator based on interval Pythagorean triangular fuzzy numbers. AIMS Mathematics, 2023, 8(11): 26237-26259. doi: 10.3934/math.20231338
    [8] Attaullah, Shahzaib Ashraf, Noor Rehman, Asghar Khan, Muhammad Naeem, Choonkil Park . Improved VIKOR methodology based on q-rung orthopair hesitant fuzzy rough aggregation information: application in multi expert decision making. AIMS Mathematics, 2022, 7(5): 9524-9548. doi: 10.3934/math.2022530
    [9] Muhammad Danish Zia, Esmail Hassan Abdullatif Al-Sabri, Faisal Yousafzai, Murad-ul-Islam Khan, Rashad Ismail, Mohammed M. Khalaf . A study of quadratic Diophantine fuzzy sets with structural properties and their application in face mask detection during COVID-19. AIMS Mathematics, 2023, 8(6): 14449-14474. doi: 10.3934/math.2023738
    [10] Gözde Yaylalı Umul . A multi-attribute group decision-making algorithm based on soft intervals that considers the priority rankings of group members on attributes of objects, along with some applications. AIMS Mathematics, 2025, 10(3): 4709-4746. doi: 10.3934/math.2025217
  • Neuropeptide S (NPS), which is a peptide that is involved in the regulation of the stress response, seems to be relevant to the mechanism of action of antidepressants that have anxiolytic properties. However, to date, there have been no reports regarding the effect of long-term treatment with escitalopram or venlafaxine on the NPS system under stress conditions.

    This study aimed to investigate the effects of the above-mentioned antidepressants on the NPS system in adult male Wistar rats that were exposed to neonatal maternal separation (MS).

    Animals were exposed to MS for 360 min. on postnatal days (PNDs) 2–15. MS causes long-lasting behavioral, endocrine and neurochemical consequences that mimic anxiety- and depression-related features. MS and non-stressed rats were given escitalopram or venlafaxine (10mg/kg) IP from PND 69 to 89. The NPS system was analyzed in the brainstem, hypothalamus, amygdala and anterior olfactory nucleus using quantitative RT-PCR and immunohistochemical methods.

    The NPS system was vulnerable to MS in the brainstem and amygdala. In the brainstem, escitalopram down-regulated NPS and NPS mRNA in the MS rats and induced a tendency to reduce the number of NPS-positive cells in the peri-locus coeruleus. In the MS rats, venlafaxine insignificantly decreased the NPSR mRNA levels in the amygdala and a number of NPSR cells in the basolateral amygdala, and increased the NPS mRNA levels in the hypothalamus.

    Our data show that the studied antidepressants affect the NPS system differently and preliminarily suggest that the NPS system might partially mediate the pharmacological effects that are induced by these drugs.



    Decision-making is a crucial task in almost all daily activities since it is highly related to cognitive thinking. Decisions are made based on available knowledge and understandable information. Most of the time, the information is indefinite and imperfect to some decision makers, leading to imprecise conclusions. The decisions are also highly influenced by the decision makers' intuitions and personal biases. According to [1], as normal human beings, decision makers are always restricted to the level of competency, psychological biases, and insufficient information.

    Zadeh [2] proposed the concept of Z-numbers as a means of overcoming this issue. Generally, Z-numbers are composed of two components, namely the restriction and reliability parts. The restriction part restricts the value that a variable can take, while the reliability part describes the degree of certainty of the restriction. Z-numbers are also described as a pair of two fuzzy numbers, which are expressed in a natural language. According to [3], Z-numbers have a higher level of generality than fuzzy numbers, intervals, and crisp values. Besides, Z-numbers have a high-level computational complexity since the arithmetic operations must deal with two fuzzy numbers in pairs [3]. The decision-making information is usually expressed in the natural language and is always imperfect. Hence, the application of Z-numbers in decision-making is essential as they better depict imperfect information, which is as close as possible to the natural language [4].

    Correspondingly, many decision-making methods have been developed based on Z-numbers such as the Analytic Hierarchy Process (AHP) [5], Technique for Order of Preferences by Similarity to Ideal Solution (TOPSIS) [6,7], Decision-Making Trial and Evaluation Laboratory (DEMATEL) [8], Weighted Aggregated Sum Product Assessment (WASPAS) [9], including the full consistency method and multi-attributive border approximation area comparison [10], Viekriterijumsko Kompromisno Rangiranje (VIKOR) [11], Approximate calculation method (ACM) [12], Elimination and Choice Translating Reality (ELECTRE) [13], Stepwise Weight Assessment Ratio Analysis (SWARA) [14], and Combinative Distance-based Assessment (CODAS) [15].

    Kang et al. [16], for instance, converted Z-numbers into regular fuzzy numbers using the fuzzy expectation of fuzzy numbers. In their method, the reliability part was converted into a weight, which was then added to the restriction part. However, it should be noted that converting Z-numbers into regular fuzzy numbers does not preserve the initial decision information in form of pairs of fuzzy numbers, which finally leads to a significant loss of information [3].

    Furthermore, Aliev et al. [17,18] proposed the arithmetic operations of Z-numbers, which allow for direct calculation without the need to convert them into regular fuzzy numbers. Essentially, the advantage of this approach is that it preserves the Z-numbers and avoids the loss of initial information. However, working directly with Z-numbers, which extensively include linear programming, leads to high computational complexity [3]. Hence, the bandwidth method was suggested in [19] to perform the operations between Z-numbers, especially on a larger scale.

    Many methods were also developed to rank fuzzy numbers. The ranking based on the centroid and spread of fuzzy numbers was used in [20], in which Z-numbers were first converted into regular fuzzy numbers. According to Abdullahi et al. [3], this conversion has caused information loss. Alternatively, Jiang et al. [21] defined a score function that considers the centroid point, the Minkowski degree of fuzziness and spread. The score function was calculated for both the restriction and reliability components and combined altogether to obtain the final ranking of Z-numbers.

    Meanwhile, using the conversion of Z-numbers into regular fuzzy numbers, Mohamad et al. [22] calculated the score value of the standardized defuzzified fuzzy number; however, the weakness of this method lies in its impurity of Z-numbers, which has undergone the transformation process. Recently, Farzam et al. [23] defined the magnitude of Z-numbers to determine their ranking. In their method, the magnitudes of restriction and reliability components were combined using the convex compound to avoid the conversion of Z-numbers into regular fuzzy numbers.

    Nevertheless, in the existing ranking methods of Z-numbers, it was proposed that the Z-numbers were either converted into regular fuzzy numbers before the final ranking was calculated or the ranking functions of the restriction and reliability components of Z-numbers were first calculated before being combined to obtain the final ranking. Since transforming Z-numbers into regular fuzzy numbers has caused a great loss of information [3], ranking methods that use this transformation process are, therefore, not really reliable.

    Fuzzy numbers are usually used to represent the linguistic terms in the decision-making information. In this regard, when ranking such fuzzy numbers, there is a reference point to which the fuzzy numbers are compared. Furthermore, the distance between the fuzzy numbers and the reference point measures which fuzzy numbers should also be ranked higher. Therefore, a new ranking method that works directly on both the components of Z-numbers is proposed in this research, in which the spread and distances of fuzzy numbers from a reference point, namely origin, are considered. The following entails some novelties of this research:

    (a) The proposed ranking method is based on the vectorial distances of fuzzy numbers from the origin. The defined distances measure how much the fuzzy numbers are distant from the origin, which will then determine their ranking. This concept is highly suitable when comparing fuzzy numbers that represent the linguistic terms with ordinal scales, which determine the decision maker's level of importance of criteria and alternatives. Moreover, the spread of the fuzzy numbers is also considered in the ranking process to make a difference in the size of the fuzzy numbers, which is closely related to the level of fuzziness such that it works synergically with the defined vectorial distance.

    (b) The employment of the convex compound in defining the final ranking of Z-numbers could avoid the loss of information when processing the decision information. Using the proposed method, the Z-numbers are not converted into regular fuzzy numbers but are processed separately on their restriction and reliability components, which are further combined using the convex compound. A parameter is defined in the convex compound to ensure that the weightage of the restriction component is at least equal to that of the reliability component.

    (c) The proposed ranking method is further integrated into the development of a novel Z-number-based AHP-WASPAS. The Z-AHP is used to quantify the criteria weights considering the decision maker's reliability, while the alternatives are ranked using the Z-WASPAS. As a validation, a numerical example from a real case study was employed to illustrate the proposed Z-AHP-WASPAS model.

    In this paper, a novel method of ranking Z-numbers is proposed based on the vectorial distances and spread of fuzzy numbers. The ranking of both the restriction and reliability components was combined using a convex compound, which prioritizes the restriction part for ranking the Z-numbers. The proposed method was validated using some empirical examples and a comparative analysis was then performed to observe the comparison of the proposed ranking method with the existing methods. A novel AHP-WASPAS model was also developed based on the proposed ranking method of Z-numbers and the real case example was adopted from [9] to illustrate the proposed model.

    In this section, the existing methods of ranking Z-numbers are reviewed to give an overview of the strengths and weaknesses of the methods. Hence, the novelty of the newly proposed ranking method can be highlighted in the next section. Assume that Z=(A,R)=(a1,a2,a3,a4;hA),(r1,r2,r3,r4;hR).

    In [20], Bakar and Gegov ranked Z-numbers based on the horizontal and vertical centroid, including spread. Three steps were developed to construct the final ranking index, as follows:

    Step 1: The centroid index for A is calculated using (1) and (2) for the horizontal and vertical axes, respectively,

    xA=xf(x)dxf(x)dx (1)
    yA=hA0α|aiα|dαhA0|aiα|dα (2)

    where |aiα| is the length of α-cuts of A.

    Step 2: The spread of A is calculated using (3).

    sA=|a4a1|×yA. (3)

    Step 3: The final ranking function then combines the horizontal and vertical centroid with the spread, as shown in (4).

    sA=xA×yA×(1sA). (4)

    Mohamad et al. [22] proposed the ordering of Z-numbers via conversion into regular fuzzy numbers. The fuzzy numbers are standardized and defuzzified before calculating the fuzzy score, considering the spread. Suppose the Z-numbers are represented by Z=(A,R)=(a1,a2,a3),(r1,r2,r3), the conversion into crisp numbers is shown in (5).

    α=xμRdxμRdx. (5)

    The weight from (5) is then added to A to obtain the weighted Z-number as shown in (6).

    Aα={x,μAα(x)|μAα=αμAα(x),x[0,1]}. (6)

    Hence, a generalized fuzzy number is obtained as Aα=(a1,a2,a3;hA) where α=hA. This generalized fuzzy number is then standardized as shown in (7),

    ˜A=(a1k,a2k,a3k;hA)=(˜a1,˜a2,˜a3;hA) (7)

    where k=maxij(|aij|,1). Subsequently, the standardized generalized fuzzy number is defuzzified, as shown in (8), and its spread is calculated as shown in (9).

    xA=˜a1+˜a2+˜a33 (8)
    sA=((˜a1xA)2+(˜a2xA)2+(˜a3xA)23)2. (9)

    Hence, the final ranking score can be calculated as

    Rank(A)=xA×hA1+sA. (10)

    In [24], Chutia proposed a new method of ranking Z-numbers based on the value and ambiguity at decision-making levels. Firstly, the values Vα(Ai),Vα(Ri) and ambiguities Aα(Ai),Aα(Ri) are calculated. Next, their distances from the reference point (0, 0) are also calculated as shown in (11).

    (dV)α=Vα(Ai)2+Vα(Ri)2,(dA)α=Aα(Ai)2+Aα(Ri)2. (11)

    Subsequently, the value index and ambiguity index are constructed at the decision level α as shown in (12) and (13), respectively.

    (IV)α=Vα(Ai)+2(dV)α3 (12)
    (IA)α=Aα(Ai)+2(dA)α3. (13)

    Finally, the following ranking rules are used to rank Z-numbers based on their value and ambiguity indices such that

    (i) (IV)α(Z1)>(IV)α(Z2)Z1Z2;

    (ii) (IV)α(Z1)<(IV)α(Z2)Z1Z2; and

    (iii) if (IV)α(Z1)=(IV)α(Z2), then

    (IA)α(Z1)>(IA)α(Z2)Z1Z2

    (IA)α(Z1)<(IA)α(Z2)Z1Z2

    (IA)α(Z1)=(IA)α(Z2)Z1Z2.

    Farzam et al. [23] used the magnitude of fuzzy numbers to rank Z-numbers. The convex compound is used to combine the restriction and reliability components, in which a parameter λ is used to control the weightage of each component. However, the parameter λ was set such that the restriction component majorly determines the ranking of Z-numbers. The magnitude of A is given by

    Mag(A)=(3hA2+2)(a2+a3)12hA+(3hA2)(a1+a4)12hA (14)

    while the magnitude of R is given by

    Mag(R)=(3hR2+2)(r2+r3)12hR+(3hR2)(r1+r4)12hR. (15)

    Hence, the final ranking of Z-numbers is determined by a ranking function that combines Mag(A) and Mag(R), as shown in (16).

    Rank(Zi)=λMag(Ai)+(1λ)Mag(Ri). (16)

    In this section, a novel synergic ranking method of fuzzy Z-numbers based on the vectorial distance and spread of fuzzy numbers representing the restriction and reliability components of Z-numbers is proposed. Some numerical examples are also explicated, followed by the comparative analysis with the previous ranking methods of Z-numbers.

    A fuzzy number can be regarded as a shape on the vectorial plane in which the distance of all vertices of such a shape can be calculated as vectorial distances with respect to the origin. Suppose a point is located on a vectorial xy-plane as shown in Figure 1, then the vectorial distance of the point can be calculated as

    distance=b2+h2. (17)
    Figure 1.  A vectorial distance on the xy-plane.

    If point b lies on the x-axis in which b>0, then its vectorial distance is simply given by

    distance=b2+02=b2=|b|=b. (18)

    Hence, if the fuzzy number entails a triangular fuzzy number as shown in Figure 2, then its average of vectorial distances is given by the mean of vectorial distances of three vertices a, b, and c from the origin, as shown in (19). Generally, positive fuzzy numbers are often used in the application for solving decision-making problems. The farther the values deviate from the origin, the larger their values, which subsequently determine the larger fuzzy numbers. Hence, the distance of the fuzzy numbers from the origin is a strong reason for defining the ranking of fuzzy numbers. Likewise, the same concept is applied to the heights of the fuzzy numbers, in which the origin is set as a reference point to determine the ranking of fuzzy numbers since fuzzy numbers with longer heights are ranked higher, which are mainly characterized by their maximum membership values.

    distance=13(a+b2+h2+c). (19)
    Figure 2.  Vectorial distance and spread of a triangular fuzzy number.

    The spread of such triangular fuzzy numbers can be assumed as the difference between points c and a. Hence, combining the vectorial distances and spread of the triangular fuzzy number A=(a,b,c;h) synergically, its ranking can be defined as follows:

    Rank(A)=13(a+b2+h2+c1+ca). (20)

    In most cases, trapezoidal fuzzy numbers are used in decision-making instead of triangular fuzzy numbers due to their ability to process ill-defined quantities [25]. Hence, the triangular fuzzy number A can be generalized into a trapezoidal fuzzy number A=(a,b,c,d;h) as shown in Figure 3, in which its rank is defined by

    Rank(A)=16(2a+b2+h2+c2+h2+2d1+da)×(1+cb). (21)
    Figure 3.  Vectorial distance and spread of a trapezoidal fuzzy number.

    Remark: The ranking of the trapezoidal fuzzy number denotes a generalization of the triangular fuzzy numbers.

    Proof. The trapezoidal fuzzy number is reduced to the triangular fuzzy number when b=c. Substituting this equality in (5) yields

    Rank(A)=16(2a+b2+h2+b2+h2+2d1+da)×(1+bb)=16(2a+2b2+h2+2d1+da)×1=13(a+b2+h2+d1+da)

    in which the final result is equivalent to (20). Hence, the rank of the trapezoidal fuzzy number is reduced to the rank of the triangular fuzzy number.

    A Z-number is a pair of fuzzy numbers, Z=(A,R), in which A represents the restriction part while R describes how reliable the first part is. Both components of Z-numbers can be assumed as triangular fuzzy numbers, as shown in Figure 4.

    Figure 4.  A Z-number: (a) restriction part; (b) reliability part.

    In this paper, a novel method of ranking Z-numbers, Z=(A,R)=(a1,a2,a3;hA),(r1,r2,r3;hR) was proposed by combining the restriction and reliability parts using a convex compound as shown in (22),

    Rank(Z)=λRank(A)+(1λ)Rank(R) (22)

    where λ takes any value in the interval [0.5, 1]. This condition governs the compound such that the restriction part, A, majorly represents the Z-number rather than the reliability part, R [23]. Rank(A) and Rank(R) in (22) constitute the ranking of triangular fuzzy numbers A and R based on the vectorial distance and spread as shown in (23) and (24), respectively.

    Rank(A)=13(a1+a22+hA2+a31+a3a1) (23)
    Rank(R)=13(r1+r22+hR2+r31+r3r1). (24)

    If both components of Z-numbers are represented by trapezoidal fuzzy numbers, then the ranking function in (21) will replace both (23) and (24). Next, the following rules are used to rank Z-numbers based on (22):

    (i) If Rank(Z1)>Rank(Z2), then Z1Z2 (Z1 is ranked higher than Z2)

    (ii) If Rank(Z1)<Rank(Z2), then Z1Z2 (Z1 is ranked lower than Z2)

    (iii) If Rank(Z1)=Rank(Z2), then Z1Z2 (Z1 is ranked the same as Z2).

    The proposed ranking of Z-numbers was subsequently validated using some numerical examples, which entail sets of Z-numbers taken from [24,26]. Table 1 displays the sets of Z-numbers used for the validation of the proposed ranking method.

    Table 1.  Sets of examples of Z-numbers [24,26].
    Set Restriction Part Reliability Part
    1.1 A1=(0.1, 0.3, 0.5;1.0) R1=(0.1, 0.3, 0.5;1.0), R2=(0.2, 0.3, 0.4;1.0)
    1.2 A1=(0.1, 0.3, 0.5;1.0) R3=(0.1, 0.2, 0.4, 0.5;1.0), R4=(0.1, 0.3, 0.5;1.0)
    1.3 A1=(0.1, 0.3, 0.5;1.0) R5=(0.1, 0.3, 0.5;0.8), R6=(0.1, 0.3, 0.5;1.0)
    1.4 A1=(0.1, 0.3, 0.5;1.0) R7=(0.1, 0.2, 0.4, 0.5;1.0), R8=(0.1, 0.3, 0.5;0.8)
    1.5 A1=(0.1, 0.3, 0.5;1.0) R9=(0.1, 0.2, 0.4, 0.5;1.0), R10=(0.3, 0.3, 0.3;1.0)
    1.6 A1=(0.1, 0.3, 0.5;1.0) R11=(0.1, 0.3, 0.5;1.0), R12=(0.3, 0.3, 0.3;1.0)
    2.1 A2=(0.1, 0.4, 0.6;1.0) R13=(0.1, 0.4, 0.5;1.0), R14=(0.2, 0.3, 0.6;1.0)
    2.2 A2=(0.1, 0.4, 0.6;1.0) R15=(0.1, 0.4, 0.7;1.0), R16=(0.2, 0.3, 0.5, 0.6;1.0)
    2.3 A2=(0.1, 0.4, 0.6;1.0) R17=(0.2, 0.3, 0.4, 0.5;1.0), R18=(0.2, 0.3, 0.5, 0.6;1.0)
    3.1 A3=(0.1, 0.4, 0.6;1.0) R19=(0.1, 0.3, 0.5;1.0), R20=(0.3, 0.5, 0.7;1.0)
    3.2 A3=(0.1, 0.4, 0.6;1.0) R21=(0.1, 0.2, 0.4, 0.5;1.0), R22=(1.0, 1.0, 1.0;1.0)
    3.3 A3=(0.1, 0.4, 0.6;1.0) R23=(0.4, 0.5, 1.0;1.0), R24=(0.4, 0.7, 1.0;1.0), R25=(0.4, 0.9, 1.0;1.0)

     | Show Table
    DownLoad: CSV

    The weightages for λ used for the empirical validation are 0.5, 0.7, and 0.9 to show that the proposed ranking method is reasonable for several situations: λ = 0.5 means that the rank of Z-numbers is balanced by both components; λ = 0.7, 0.9 means that the rank of the first component is higher than the second one; λ = 1.0 is not considered in this case because it reduces the Z-numbers to regular fuzzy numbers since the reliability part has completely vanished. Table 2 displays the ranking results obtained using the proposed method and their comparisons with existing methods.

    Table 2.  Sets of examples of Z-numbers [24,26].
    Set Proposed [20] [21] [22] [27] [28] [24] [29] [23]
    1.1 Z1Z2 Z1~Z2 Z1Z2 Z1~Z2 Z1~Z2 Z1~Z2 Z1Z2 Z1Z2 Z1~Z2
    1.2 Z1Z2 Z1~Z2 Z1Z2 Z1~Z2 Z1~Z2 Z1~Z2 Z1Z2 Z1~Z2 Z1~Z2
    1.3 Z1Z2 Z1~Z2 Z1Z2 Z1~Z2 Z1~Z2 Z1~Z2 Z1Z2 Z1~Z2 Z1Z2
    1.4 Z1Z2 Z1~Z2 Z1Z2 Z1~Z2 Z1~Z2 Z1~Z2 Z1Z2 Z1~Z2 Z1Z2
    1.5 Z1Z2 Z1~Z2 Z1Z2 Z1~Z2 Z1~Z2 Z1~Z2 Z1Z2 Z1~Z2 Z1~Z2
    1.6 Z1Z2 Z1~Z2 Z1Z2 Z1~Z2 Z1~Z2 Z1~Z2 Z1Z2 Z1Z2 Z1~Z2
    2.1 Z1Z2 Z1Z2 Z1Z2 Z1Z2 Z1Z2 Z1Z2 Z1Z2 Z1Z2 Z1Z2
    2.2 Z1Z2 Z1~Z2 Z1Z2 Z1~Z2 Z1~Z2 Z1~Z2 Z1Z2 Z1Z2 Z1~Z2
    2.3 Z1Z2 Z1~Z2 Z1Z2 Z1~Z2 Z1~Z2 Z1~Z2 Z1Z2 Z1Z2 Z1Z2
    3.1 Z1Z2 Z1Z2 Z1Z2 Z1Z2 Z1Z2 Z1Z2 Z1Z2 Z1Z2 Z1Z2
    3.2 Z1Z2 Z1Z2 Z1Z2 Z1Z2 Z1Z2 Z1Z2 Z1Z2 Z1Z2 Z1Z2
    3.3 Z1Z2
    Z3
    Z1Z2
    Z3
    Z1Z2
    Z3
    Z1Z2
    Z3
    Z1Z2
    Z3
    Z1Z2
    Z3
    Z1Z2
    Z3
    Z1~Z2
    ~Z3
    Z1Z2
    Z3

     | Show Table
    DownLoad: CSV

    For Example 1.1, both R1 and R2 are triangular fuzzy numbers having the same central value with different spreads, as shown in Figure 5(a). According to [30], fuzzy sets with higher means and smaller spreads are preferred. Hence, theoretically through Z2Z1 and by using the proposed method, the same result was obtained. The ranking methods from [21,24,29] also ranked Z2 higher than Z1, whereas Z1 is of the same rank as Z2 using the methods from [20,22,23,27,28].

    Figure 5.  Example 1: (a) set 1.1; (b) set 1.2; (c) set 1.3; (d) set 1.4; (e) set 1.5; (f) set 1.6.

    Example 1.2 compares the triangular and trapezoidal fuzzy numbers with the same spread. The proposed method ranked Z1Z2, similar to [21], which indicates that the trapezoidal fuzzy number is ranked higher than the triangular fuzzy number since the triangular fuzzy number only contains a single point with the highest membership value. This is also supported by the fact that the trapezoidal fuzzy number has a better ability to process ill-defined quantities [25].

    In Example 1.3, two triangular fuzzy numbers with different heights are compared. In reference to Figure 5(c), Z2Z1 since Z2 clearly has a higher maximum membership value than Z1 and the same result was obtained using the proposed ranking method. On the other hand, using the ranking of Z-numbers proposed in [20,22,27,28,29], the ranking result Z1~ Z2 was obtained.

    Example 1.4 ranked Z1 greater than Z2, in which Z1 is a trapezoidal fuzzy number with higher maximum membership values. Using the magnitude of Z-numbers [23], value and ambiguity [24], and centroid, fuzziness degree, and spreads of fuzzy numbers [21], Z1Z2 was also obtained. In Example 1.5, the trapezoidal fuzzy number (Z1) was compared to a singleton (Z2) and the proposed ranking based on vectorial distance and spread ranked Z2 higher than Z1. The same result was also obtained in [21,24] due to the fact that the singleton is a crisp value, which does not have a degree of fuzziness. Moreover, the same result was also obtained when the singleton was compared to the triangular fuzzy numbers, as illustrated in Example 1.6.

    Example 2.1 compares two triangular fuzzy numbers with different spreads; one is farther from the origin, while the other is nearer to the origin. Since they share the same length of spread, vectorial distances of vertices were used to determine the rank of fuzzy numbers. Hence, Z2Z1 was obtained using the proposed method. The same result was also obtained using the existing ranking methods of Z-numbers, except for the magnitude proposed in [23], in which Z1 was ranked higher.

    In Example 2.2 as illustrated in Figure 6(b), the trapezoidal fuzzy number (Z2) was ranked higher than the triangular fuzzy number (Z1). This is supported by the fact that the trapezoidal fuzzy number has a smaller spread and many points with maximum membership values. The same ranking result was also obtained using the methods from [21,29]. Example 2.3 illustrates two trapezoidal fuzzy numbers with different spreads, in which Z1 was ranked higher since it has a smaller spread than Z2. This is supported by the fact that fuzzy numbers with smaller spreads are preferred [30].

    Figure 6.  Example 2: (a) set 2.1; (b) set 2.2; (c) set 2.3.

    In reference to Figure 7, Example 3.1 ranked Z2Z1 since the position of Z2 is farther from the origin compared to Z1 although they have the same spread length. In this case, the vectorial distances determine the ranking of the triangular fuzzy numbers. The same result was obtained in [20,21,22,23,24,27,28,29]. Meanwhile, in Example 3.2, the singleton was compared to the trapezoidal fuzzy number, in which the singleton is extensively farther from the origin compared to the trapezoidal fuzzy number. Hence, the proposed method ranked the singleton (Z2) higher than the trapezoidal fuzzy number (Z1). A similar result was also obtained from the existing methods of ranking Z-numbers, except for the method from [29].

    Figure 7.  Example 3: (a) set 3.1; (b) set 3.2; (c) set 3.3.

    In Example 3.3, three triangular fuzzy numbers that share the same spread were compared. Since Z1 is the nearest to the origin, it is ranked the lowest, followed by Z2 and Z3. In this situation, the vectorial distance of the peak of the triangular fuzzy numbers majorly determines the ranking order. The same ranking result was also obtained using existing methods of ranking Z-numbers, except [29]. According to [29], the three triangular fuzzy numbers have the same ranking.

    AHP-WASPAS is extended to Z-number's application in obtaining criteria weights and ranking desired alternatives. This proposed model will utilize the ranking approach based on the vectorial distances and spread of Z-numbers to defuzzify the decision information into crisp values. The AHP model was used to obtain the criteria weights, while the WASPAS model was developed to rank the alternatives. The following entails the detailed steps of the proposed AHP-WASPAS model:

    Step 1: Construct the hierarchical structure consisting of three layers: the top layer is the aim of the decision-making problem, the middle layer consists of the criteria or attributes, and the bottom layer lists all the alternatives.

    Step 2: Obtain the decision information from the decision maker using pairwise comparison matrices as shown in (25). Note that (aij,rij) is a Z-number in which aij and rij represent the restriction and reliability, respectively, on the degree of importance that the i-th criterion is preferred to the j-th criterion. From this point onwards, aij and rij are both treated as triangular fuzzy numbers, denoted by (aij1,aij2,aij3) and (rij1,rij2,rij3), respectively. Hence, all arithmetic operations involving these elements are based on the arithmetic operations of triangular fuzzy numbers.

    ((a11,r11)(a12,r12)(a1n,r1n)(a21,r21)(a22,r22)(a2n,r2n)(an1,rn1)(an2,rn2)(ann,rnn)). (25)

    Step 3: The fuzzy numbers representing restriction and reliability are separately aggregated using the defined operator in (26),

    Φ((ai1,ri1),(ai2,ri2),...,(ain,rin))=((ai1+...+ain),(ri1+...+rin))=(˜ai,˜ri) (26)

    where Φ is the arithmetic aggregation operators and ai1,...,ain,ri1,...,rin are all triangular fuzzy numbers. Meanwhile, (˜ai,˜ri) is the aggregated triangular fuzzy number.

    Step 4: The fuzzy weights are then evaluated using the formula below,

    (Ai,Ri)=(˜ai(ni=1˜ai)1,˜ri(ni=1˜ri)1) (27)

    where (ni=1˜ai)1 and (ni=1˜ri)1 are the inverses of the triangular fuzzy numbers.

    Step 5: The fuzzy weights (Ai,Ri) are then defuzzified into Rank(Zi) using (22) for all i=1,2,...,n. Hence, the final weights, W(Zi), are obtained by normalizing Rank(Zi) using the formula

    W(Zi)=Rank(Zi)ni=1Rank(Zi), (28)

    such that W(Z1)+W(Z2)+...+W(Zn)=1.

    Step 6: Next, the decision maker's evaluation of each alternative with respect to all criteria is obtained as shown in (29),

    ((b11,r11)(b12,r12)(b1n,r1n)(b21,r21)(b22,r22)(b2n,r2n)(bm1,rm1)(bm2,rm2)(bmn,rmn)), (29)

    where (bij,rij) is a Z-number in which bij and rij represent restriction and reliability, respectively, on the level of importance of the j-th criterion for the i-th alternative. Note that bij and rij are both triangular fuzzy numbers, denoted by (bij1,bij2,bij3) and (rij1,rij2,rij3), respectively.

    Step 7: The decision matrix (29) is normalized using

    (˜bij,˜rij)=(bijmaxbij3,rijmaxrij3). (30)

    The j-th criterion is a benefit criterion and maxbij3 is the maximum value of the rightmost element in the triangular fuzzy numbers bij from each column and row. maxrij3 is defined analogously, but for the reliability component. Otherwise, the following formula is used:

    (˜bij,˜rij)=(minbij3bij,minrij3rij) (31)

    minbij3 is the minimum value of the rightmost element in the triangular fuzzy numbers bij from each column and row. minrij3 is defined similarly for the triangular fuzzy numbers representing the reliability components.

    Step 8: The weighted sum matrix is then constructed by evaluating the weighted sum of the normalized decision matrix using the following formula:

    (WS(˜bij),WS(˜rij))=(˜bij×W(Zj),˜rij×W(Zj)) (32)

    W(Zj) is the weight of the j-th criterion and ˜bij and ˜rij are the normalized triangular fuzzy numbers representing the restriction and reliability components, respectively, for the j-th criterion and i-th alternative. The weighted product matrix is also constructed by evaluating the weighted product of the normalized decision matrix using the following formula:

    (WP(˜bij),WP(˜rij))=(˜bijW(Zj),˜rijW(Zj)). (33)

    Step 9: The utility function combining the weighted sum and weighted product for the i-th alternative is calculated using the following formula:

    (Bi,Ri)=(σmj=1WS(˜bij)+(1σ)mj=1WP(˜bij),σmj=1WS(˜rij)+(1σ)mj=1WP(˜rij)) (34)

    mj=1WS(˜bij) and mj=1WS(˜rij) are the summation of the weighted sum of fuzzy numbers for all criteria, while mj=1WP(˜bij) and mj=1WP(˜rij) are the product of the weighted product of fuzzy numbers for all criteria, and σ[0,1].

    Step 10: Finally, the Z-numbers (Bi,Ri) representing the utility functions are defuzzified into Rank(Zi) using (22). The alternatives are then ranked based on the calculated defuzzified values. The greater the defuzzified value, the higher the alternative is ranked and vice versa.

    The developed steps for the Z-AHP-WASPAS above are summarized and illustrated in Figure 8.

    Figure 8.  The proposed Z-AHP-WASPAS.

    The proposed Z-AHP-WASPAS model was subsequently implemented in the prioritization of public services for the implementation of Industry 4.0 tools adopted from [9].

    Step 1: The hierarchical structure is first constructed as shown in Figure 9.

    Figure 9.  AHP hierarchical structure.

    Step 2: The decision information on the pairwise comparison matrix is obtained as displayed in Table 3.

    Table 3.  Pairwise comparison matrix of AHP.
    Criterion C1 C2 C3 C4 C5 C6
    C1 (1, 9) (1/2, 4) (1/3, 5) (1/3, 5) (4, 7) (2, 7)
    C2 (2, 7) (1, 9) (1/2, 4) (1/2, 4) (4, 7) (3, 5)
    C3 (3, 5) (2, 7) (1, 9) (2, 7) (5, 8) (3, 5)
    C4 (3, 5) (2, 7) (1/2, 4) (1, 9) (4, 7) (3, 5)
    C5 (1/4, 4) (1/4, 4) (1/5, 2) (1/4, 4) (1, 9) (1/2, 4)
    C6 (1/2, 4) (1/3, 5) (1/3, 5) (1/3, 5) (2, 7) (1, 9)

     | Show Table
    DownLoad: CSV

    The decision information in Table 3 is subsequently converted into Z-numbers, in which the restriction and reliability components will be represented by triangular fuzzy numbers that correspond to the crisp values, as shown in Table 4.

    Table 4.  Z-Numbers representation for the restriction and reliability components.
    Crisp Fuzzy Numbers (Restriction) Crisp Fuzzy Numbers (Reliability)
    1 (1, 1, 1) 1 (0.0, 0.1, 0.2)
    2 (1, 3, 5) 2 (0.1, 0.2, 0.3)
    3 (3, 5, 7) 3 (0.2, 0.3, 0.4)
    4 (5, 7, 9) 4 (0.3, 0.4, 0.5)
    5 (7, 9, 9) 5 (0.4, 0.5, 0.6)
    1/2 (1/5, 1/3, 1) 6 (0.5, 0.6, 0.7)
    1/3 (1/7, 1/5, 1/3) 7 (0.6, 0.7, 0.8)
    1/4 (1/9, 1/7, 1/5) 8 (0.7, 0.8, 0.9)
    1/5 (1/9, 1/9, 1/7) 9 (1.0, 1.0, 1.0)

     | Show Table
    DownLoad: CSV

    Step 3: The Z-numbers for all criteria are aggregated horizontally using the operator in (26). For example, when the Z-numbers representing C1 are aggregated, the following calculation is performed:

    (1,1,1)+(1/5,1/3,1)+(1/7,1/5,1/3)+(1/7,1/5,1/3)+(5,7,9)+(1,3,5)=(1+15+17+17+5+1,1+13+15+15+7+3,1+1+13+13+9+5)=(7.486,11.733,16.667)
    (1.0,1.0,1.0)+(0.3,0.4,0.5)+(0.4,0.5,0.6)+(0.4,0.5,0.6)+(0.6,0.7,0.8)+(0.6,0.7,0.8)=(1.0+0.3+0.4+0.4+0.6+0.6,1.0+0.4+0.5+0.5+0.7+0.7,1.0+0.5+0.6+0.6+0.8+0.8)=(3.300,3.800,4.300)

    Hence, the aggregated Z-number for C1 is obtained as ((7.486, 11.733, 16.667), (3.3, 3.8, 4.3)). Additionally, the Z-numbers for the rest of the criteria are aggregated analogously and the results are presented in Table 5.

    Table 5.  Aggregated Z-numbers.
    Criterion Aggregated Z-Numbers
    C1 ((7.486, 11.733, 16.667), (3.300, 3.800, 4.300))
    C2 ((10.400, 16.667, 24.000), (3.200, 3.700, 4.200))
    C3 ((16.000, 26.000, 34.000), (3.700, 4.200, 4.700))
    C4 ((13.200, 21.333, 30.000), (3.300, 3.800, 4.300))
    C5 ((1.644, 1.873, 2.743), (2.300, 2.800, 3.300))
    C6 ((2.629, 4.933, 8.000), (3.100, 3.600, 4.100))

     | Show Table
    DownLoad: CSV

    Step 4: The fuzzy weight for each criterion is then calculated using (27) and the results are presented in Table 6. For example, the calculation for obtaining the fuzzy weight for C1 will be shown. The sum of the aggregated Z-numbers is first obtained by summing up all the aggregated Z-numbers from Table 5 and the total is ((51.359, 82.540,115.410), (18.9, 21.9, 24.9)). Subsequently, the inverse of such numbers is calculated as follows:

    (51.359, 82.540, 115.410)1=(1115.410,182.540,151.359)=(0.0087, 0.0121, 0.0195)(18.9, 21.9, 24.9)1=(124.9,121.9,118.9)=(0.0402, 0.0457, 0.0529)
    Table 6.  Fuzzy weights.
    Criterion Fuzzy Weights Rank(A) Rank(R)
    C1 ((0.065, 0.142, 0.325), (0.133, 0.174, 0.228)) 0.370 0.419
    C2 ((0.090, 0.202, 0.467), (0.129, 0.169, 0.222)) 0.382 0.416
    C3 ((0.139, 0.315, 0.662), (0.149, 0.192, 0.249)) 0.405 0.429
    C4 ((0.114, 0.258, 0.584), (0.133, 0.174, 0.228)) 0.393 0.419
    C5 ((0.014, 0.023, 0.053), (0.092, 0.128, 0.175)) 0.343 0.393
    C6 ((0.023, 0.060, 0.156), (0.124, 0.164, 0.217)) 0.347 0.413

     | Show Table
    DownLoad: CSV

    Next, the fuzzy weight for C1 can be obtained by multiplying the aggregated Z-number for C1 with the obtained inverse triangular fuzzy number, as shown below.

    (7.486, 11.733, 16.667)×(0.0087, 0.0121, 0.0195)=(7.486×0.0087, 11.733×0.0121, 16.667×0.0195)=(0.065, 0.142, 0.325)
    (3.30, 3.80, 4.30)×(0.0402, 0.0457, 0.0529)=(3.30×0.0402, 3.80×0.0457, 4.30×0.0529)=(0.133, 0.174, 0.228)

    Step 5: The restriction and reliability components of the obtained fuzzy weights from the previous step are then defuzzified. As an illustration, the calculation for defuzzifying the restriction and reliability components representing the fuzzy weight of C1 is shown below.

    Rank(A)=13(0.065+0.1422+12+0.3251+0.3250.065)=0.370Rank(R)=13(0.133+0.1742+12+0.2281+0.2280.133)=0.419

    The fuzzy weights of the rest of the criteria are then defuzzified similarly as shown in Table 6.

    The defuzzified weights for the restriction and reliability components are subsequently combined using (22) by choosing λ = 0.75 to highlight that the role of the restriction component is more important than its reliability [23]. The obtained weights are then normalized using (28) and the results are presented in Table 7.

    Table 7.  Normalized weights.
    Criterion Final Weight Normalized Weight Priority Rank
    C1 0.382 0.166 4
    C2 0.390 0.170 3
    C3 0.411 0.178 1
    C4 0.399 0.173 2
    C5 0.355 0.154 6
    C6 0.364 0.158 5

     | Show Table
    DownLoad: CSV

    Step 6: The decision maker's evaluation for all alternatives with respect to each criterion is obtained as shown in Table 8.

    Table 8.  Decision information matrix of WASPAS.
    Alternative C1 C2 C3 C4 C5 C6
    A1 (5, 8) (4, 7) (5, 8) (5, 8) (4, 7) (4, 7)
    A2 (2, 5) (4, 7) (3, 6) (4, 7) (2, 5) (3, 6)
    A3 (3, 6) (3, 6) (4, 7) (4, 7) (3, 6) (4, 7)
    A4 (3, 6) (4, 7) (5, 8) (3, 6) (3, 6) (3, 6)
    A5 (4, 7) (5, 8) (4, 7) (4, 7) (3, 6) (5, 8)
    A6 (5, 8) (4, 7) (5, 8) (3, 6) (2, 5) (4, 7)

     | Show Table
    DownLoad: CSV

    The above decision matrix is further transformed into Z-numbers using the Z-numbers representation, as shown in Table 4.

    Step 7: Since all the criteria constitute benefit criteria, the decision matrix in the form of Z-numbers is, therefore, normalized using (30). Note that maxbij3=9, all elements bij in the decision matrix is consequently divided by 9. For example, b11 = (7, 9, 9) is normalized as follows:

    19(7,9,9)=(0.778, 1.000, 1.000).

    Step 8: The weighted sum and weighted product matrices are constructed using (32) and (33), respectively. Considering the normalized (˜b11,˜r11)=((0.778, 1.000, 1.000),(0.778, 0.889, 1.000)) and the criteria weight for C1, which is 0.166, the weighted sum and weighted product for (˜b11,˜r11) is, hence, calculated as follows:

    (WS(˜b11),WS(˜r11))=((0.778×0.166,1.000×0.166,1.000×0.166),(0.778×0.166,0.889×0.166,1.000×0.166))=((0.129, 0.166, 0.166), (0.129, 0.148, 0.166))
    (WP(˜b11),WP(˜r11))=((0.7780.166,1.0000.166,1.0000.166),(0.7780.166,0.8890.166,1.0000.166))=((0.959, 1.000, 1.000), (0.959, 0.981, 1.000)).

    Step 9: The utility function for each alternative is calculated using (34) by taking σ = 0.5, which represents the equal weightage for the weighted sum and weighted product. For example, the utility function for A1 will be illustrated. The total sum of the weighted sum, mj=1WS(˜bij) and the total product of the weighted product, mj=1WP(˜bij) for the restriction component are first calculated and obtained as (0.665, 0.886, 0.997) and (0.658, 0.882, 1.000), respectively. As for the reliability component, the total sum of the weighted sum, mj=1WS(˜rij) and the total product of the weighted product, mj=1WP(˜rij) are obtained as (0.720, 0.831, 0.941) and (0.721, 0.832, 0.943), respectively. Hence, the Z-numbered utility function for A1 is calculated as follows:

    (B1,R1)=(0.5×(0.665,0.886,0.997)+0.5×(0.658,0.882,1.000),0.5×(0.720,0.831,0.941)+0.5×(0.721,0.832,0.943))=((0.661, 0.884, 0.998), (0.720, 0.831, 0.942))

    Meanwhile, the defuzzification of the restriction and reliability components will be performed separately as follows:

    Rank(B1)=13(0.661+0.8842+12+0.9981+0.9980.884)=0.747Rank(R1)=13(0.720+0.8312+12+0.9421+0.9420.720)=0.808

    The utility functions of the rest of the alternatives are evaluated analogously as presented in Table 9 with their corresponding defuzzified values.

    Table 9.  Utility function values in terms of Z-numbers.
    Alternative Utility Function in Terms of Z-Numbers Rank(B) Rank(R)
    A1 ((0.661, 0.884, 0.998), (0.720, 0.831, 0.942)) 0.747 0.808
    A2 ((0.304, 0.542, 0.772), (0.554, 0.667, 0.780)) 0.502 0.689
    A3 ((0.441, 0.676, 0.913), (0.621, 0.738, 0.856)) 0.580 0.734
    A4 ((0.433, 0.665, 0.863), (0.615, 0.730, 0.845)) 0.582 0.731
    A5 ((0.572, 0.784, 0.927), (0.667, 0.772, 0.875)) 0.681 0.774
    A6 ((0.474, 0.705, 0.859), (0.633, 0.740, 0.847)) 0.615 0.748

     | Show Table
    DownLoad: CSV

    Step 10: Finally, the defuzzified restriction and reliability components of the utility functions are combined using (22), taking λ = 0.75, similar to the AHP model. Table 10 shows the final priority weights for all alternatives and their ranking.

    Table 10.  Final priority weights and ranking of alternatives.
    Alternative Final Priority Weight Priority Rank
    A1 0.762 1
    A2 0.549 6
    A3 0.618 5
    A4 0.619 4
    A5 0.704 2
    A6 0.648 3

     | Show Table
    DownLoad: CSV

    The priority ranking of alternatives obtained using the proposed Z-AHP-WASPAS model sensitivity follows similar order as [9], which is A1 > A5 > A6 > A4 > A3 > A2. The sensitivity analysis was further conducted to highlight the advantage of the proposed model compared to the previous one. Each of the criteria weights were increased by 50% and the effects on the ranking order of alternatives were observed. Table 11 shows the results for the final priority weights obtained using the proposed Z-AHP-WASPAS model when the weight of each criterion is increased by 50%.

    Table 11.  Sensitivity analysis for the proposed Z-AHP-WASPAS model.
    Alternative Criterion with Increased Weights
    C1 C2 C3 C4 C5 C6
    A1 0.804 0.754 0.754 0.754 0.755 0.755
    A2 0.551 0.558 0.551 0.551 0.550 0.550
    A3 0.618 0.618 0.634 0.618 0.618 0.618
    A4 0.619 0.619 0.619 0.636 0.619 0.619
    A5 0.701 0.701 0.700 0.701 0.730 0.701
    A6 0.647 0.647 0.647 0.647 0.647 0.668

     | Show Table
    DownLoad: CSV

    Next, the sensitivity analysis was performed on the Z-AHP-WASPAS model proposed in [9] to be compared with the results obtained using the proposed model in this paper. The results in Table 12 show that the ranking of alternatives changes when the weights of C3 and C4 are increased by 50%.

    Table 12.  Sensitivity analysis for Z-AHP-WASPAS [9].
    Alternative Criterion with Increased Weights
    C1 C2 C3 C4 C5 C6
    A1 0.891 0.871 0.907 0.898 0.887 0.884
    A2 0.532 0.567 0.527 0.580 0.547 0.548
    A3 0.642 0.633 0.676 0.665 0.650 0.654
    A4 0.679 0.694 0.769 0.650 0.689 0.684
    A5 0.766 0.785 0.754 0.760 0.765 0.772
    A6 0.752 0.741 0.806 0.691 0.736 0.742

     | Show Table
    DownLoad: CSV

    The ranking orders A1 > A6 > A4 > A5 > A3 > A2 and A1 > A5 > A6 > A3 > A4 > A2 were observed when the weights of C3 and C4 were changed, respectively. The ranking order remained unchanged when the other criteria weights were changed, resulting in a 66.67% consistency. Comparing this result to the proposed Z-AHP-WASPAS model, the ranking order maintained its stability when all criteria weights were changed, except for C3, resulting in an 83.33% consistency. In fact, only the interchange of ranking between A3 and A4 was observed when the weight of C3 was increased by 50%. The comparison of the sensitivity analysis is illustrated in Figure 10.

    Figure 10.  The radar diagram for the sensitivity analysis: (a) Proposed Z-AHP-WASPAS; (b) Z-AHP-WASPAS [9].

    The consistency of the proposed Z-AHP-WASPAS model is influenced by many factors. First, this includes the preservation of decision information in the form of Z-numbers until the final steps of the AHP and WASPAS. The proposed model does not transform the Z-numbers into regular fuzzy numbers since this process is believed to lead to a great loss of information [3]. Second, the defuzzification of Z-numbers into crisp values for the valuation of the criteria weights and priority weights of alternatives makes use of the proposed ranking approach of Z-numbers based on the vectorial distances and spread. In addition, the comparative analysis has also shown that the proposed method could rank Z-numbers better than the existing approaches. In fact, when applying the proposed method for ranking Z-numbers in the decision-making model, the sensitivity analysis has shown an improvement in consistency. Third, the use of the convex compound in combining the restriction and reliability components of Z-numbers allows the level of importance of each component to depict the Z-numbers. In this example, the variable λ was set as 0.75 to highlight that the role of the restriction component is more important than its reliability [23].

    Furthermore, the proposed Z-AHP-WASPAS model was compared with the classical AHP method in obtaining the criteria weights. For this purpose, the classical AHP based on crisp scales [31] was used. In the classical AHP, the decision maker's evaluation is kept as crisp values and the degree of reliability of the decision maker's preferences is completely ignored, as shown in Table 13.

    Table 13.  Criteria weights obtained using classical AHP.
    Criterion C1 C2 C3 C4 C5 C6 Weight
    C1 1 1/2 1/3 1/3 4 2 0.123
    C2 2 1 1/2 1/2 4 3 0.183
    C3 3 2 1 2 5 3 0.321
    C4 3 2 1/2 1 4 3 0.246
    C5 1/4 1/4 1/5 1/4 1 1/2 0.047
    C6 1/2 1/3 1/3 1/3 2 1 0.080

     | Show Table
    DownLoad: CSV

    Using the obtained criteria weights, the weighted sum and weighted product of the fuzzy WASPAS model were evaluated. The ranking of alternatives was obtained as A1 > A5 > A6 > A3 > A4 > A2. The sensitivity analysis was further performed to see the effects of increasing the weight of each criterion by 50%. Table 14 presents the results of the sensitivity analysis when the weights obtained using the classical AHP are integrated into the WASPAS model.

    Table 14.  Sensitivity analysis for the WASPAS model with criteria weights obtained using classical AHP [31].
    Alternative Criterion with Increased Weights
    C1 C2 C3 C4 C5 C6
    A1 0.754 0.726 0.721 0.724 0.729 0.728
    A2 0.502 0.508 0.509 0.506 0.501 0.502
    A3 0.594 0.591 0.653 0.587 0.598 0.596
    A4 0.585 0.584 0.582 0.622 0.587 0.586
    A5 0.685 0.686 0.688 0.687 0.679 0.685
    A6 0.633 0.634 0.640 0.637 0.631 0.618

     | Show Table
    DownLoad: CSV

    Similar to the Z-AHP-WASPAS model from [9], the ranking order changed when the weights of C3 and C4 were increased by 50%. The increase in weights for C3 and C4 resulted in the ranking orders A1 > A5 > A3 > A6 > A4 > A2 and A1 > A5 > A6 > A4 > A3 > A2, respectively. Hence, the consistency performance was only 66.67% when the criteria weights were quantified using the classical AHP and further applied in the fuzzy WASPAS.

    In general, the results are affected by the ignorance of the reliability parts, which represent the degree of sureness when the decision maker is making the evaluation. This shows that the application of Z-numbers in decision-making is essential as it can depict imperfect information. Besides, the use of crisp numbers in the pairwise comparison matrix of the classical AHP could not present the decision information in the best way. This is due to imprecision and uncertainties when the decision maker is hesitant on giving discrete values on the relative importance of the criteria. Hence, the use of fuzzy numbers can better describe the criteria preferences [32].

    However, it is still important to note that this research is limited to the application of the proposed ranking method in the Z-AHP-WASPAS model. Since the proposed ranking of Z-numbers is based on the vectorial distance and spread of fuzzy numbers, other decision-making models are based on distance such as fuzzy TOPSIS, CODAS, and evaluation based on distance from average solution (EDAS). Therefore, in future works, the proposed method should be extended to other methods, which are regressively discussed in the current decision-making methods such as preference relation [33,34,35] and the consensus model for group decision-making [36,37].

    Ranking Z-numbers is a complex task since they are fashioned by a pair of fuzzy numbers, namely the restriction and reliability components. When ranking Z-numbers, it is essential to keep the information so that it can be processed by making use of the meaning of the Z-numbers. In addition, the issue of information loss when converting Z-numbers into regular fuzzy numbers should be overcome. Hence, a novel ranking method of Z-numbers was proposed in this paper based on the vectorial distances and spread. The advantages of the study can be summarized as follows:

    (a) The vectorial distances in the proposed ranking method measure the distances of all vertices, which form the shape of fuzzy numbers from a reference point, namely the origin. The spread is also considered in ranking the Z-numbers to cater to various situations in which Z-numbers have different spreads. Besides, this ranking approach is very suitable to be adopted in any decision-making model that uses linguistic terms to describe the level of importance of criteria and alternatives. The Z-numbers, which represent the linguistic terms, are appropriately ranked based on their distances and spread from the origin.

    (b) The proposed ranking of Z-numbers does not convert them into regular fuzzy numbers but instead keeps the restriction and reliability components of the Z-numbers until a final ranking is obtained. The ranking method makes use of the convex compound to combine the restriction and reliability components in which a variable is introduced to allow for at least equal weightage for both components; however, in most situations, it is assumed that the restriction component is given more priority compared to its reliability. Hence, a comparative analysis was conducted to validate the proposed ranking method and comparison some examples of Z-numbers with the existing ranking methods. Overall, it was observed that the proposed method has a better capability of ranking Z-numbers, which could be further used in solving decision-making problems.

    (c) The ranking method of Z-numbers proposed in this study was further extended to develop a novel AHP-WASPAS model based on the Z-numbers, in which the decision information was preserved as Z-numbers and the proposed ranking method was used to defuzzify the processed Z-numbers information into crisp values to obtain the criteria weights and priority weights of alternatives. Additionally, a numerical example was also adopted to illustrate the proposed Z-AHP-WASPAS model and the sensitivity analysis was further conducted to evaluate the consistency of the model. In essence, the study observed that the proposed model has improved its consistency compared to the existing model.

    The improvement of the Z-AHP-WASPAS model using the proposed ranking approach could be influenced by several factors such as the preservation of Z-numbers information, the use of the improved ranking method of Z-numbers, and the choice of variable value in controlling the weightages of the restriction and reliability components. However, it is important to note that this research is limited to the application of the Z-number-based ranking approach in the AHP-WASPAS model. The ranking approach could be applied when developing other fuzzy decision-making models that require linguistic evaluation from decision makers. Besides, the proposed model does not consider group decision-making that involves many decision makers and consequently requires further exploration in aggregating all the decision makers' preferences, such as the consensus model. In future works, the proposed ranking approach of Z-numbers could also be applied when developing other decision-making models such as TOPSIS, DEMATEL, and Best Worst Method (BWM).

    The authors would like to thank Universiti Malaysia Pahang for laboratory facilities as well as financial support under UMP Postgraduate Research Grants Scheme (PGRS) No. PGRS220301.

    All the authors declare that there is no conflict of interest.


    Acknowledgments



    We thank Prof. Ryszard Wiaderkiewicz, Head of Department of Histology and Embryology at the Medical University of Silesia, for facilitating the histochemical analysis. The assistance of technical workers is gratefully acknowledged.
    The authors would also like to thank ADAMED (Poland) for supplying the antidepressants used in the study.

    Conflict of interest



    The authors do not declare any conflict of interest.

    Author contributions



    Conceptualization, EO and MG; investigation, MG, MZ, MP-S; technical support, AP; statistical analysis, MG; data curation, MG; writing—original draft preparation, MG; writing—review and editing, EO. All authors have read and agreed to the publishing of this version of the manuscript.

    Funding source



    This work was supported by a doctoral grant (KNW-2-046/D/7/N) and a statutory grant (KNW-1-094/N/8/O) from the Medical University of Silesia, Katowice, Poland.

    [1] Kormos V, Gaszner B (2013) Role of neuropeptides in anxiety, stress, and depression: from animals to humans. Neuropeptides 47: 401-419. https://doi.org/10.1016/j.npep.2013.10.014
    [2] Yamazoe M, Shiosaka S, Emson PC, et al. (1985) Distribution of neuropeptide Y in the lower brainstem: an immunohistochemical analysis. Brain Res 335: 109-120. https://doi.org/10.1016/0006-8993(85)90281-1
    [3] Douglas FL, Palkovits M, Brownstein MJ (1982) Regional distribution of substance P-like immunoreactivity in the lower brainstem of the rat. Brain Res 245: 376-378. https://doi.org/10.1016/0006-8993(82)90821-6
    [4] Spirovski D, Li Q, Pilowsky PM (2012) Brainstem galanin-synthesizing neurons are differentially activated by chemoreceptor stimuli and represent a subpopulation of respiratory neurons. J Comp Neurol 520: 154-173. https://doi.org/10.1002/cne.22723
    [5] Liu C, Lovenberg TW (2008) Relaxin-3, INSL5, and their receptors. Orphan G Protein-Coupled Receptors and Novel Neuropeptides, 46. Berlin, Heidelberg: Springer 213-237. https://doi.org/10.1007/400_2007_055
    [6] Palasz A, Rojczyk E, Golyszny M, et al. (2016) Long-term treatment with haloperidol affects neuropeptide S and NPSR mRNA levels in the rat brain. Acta Neuropsychiatr 28: 110-116. https://doi.org/10.1017/neu.2015.56
    [7] Pałasz A, Żarczyński P, Bogus K, et al. (2021) Modulatory effect of olanzapine on SMIM20/phoenixin, NPQ/spexin and NUCB2/nesfatin-1 gene expressions in the rat brainstem. Pharmacol Rep 73: 1188-1194. https://doi.org/10.1007/s43440-021-00267-7
    [8] Kumsta R, Chen FS, Pape HC, et al. (2013) Neuropeptide S receptor gene is associated with cortisol responses to social stress in humans. Biol Psychol 93: 304-307. https://doi.org/10.1016/j.biopsycho.2013.02.018
    [9] Smith KL, Patterson M, Dhillo WS, et al. (2006) Neuropeptide S stimulates the hypothalamo-pituitary-adrenal axis and inhibits food intake. Endocrinology 147: 3510-3518. https://doi.org/10.1210/en.2005-1280
    [10] Pape HC, Jüngling K, Seidenbecher T, et al. (2010) Neuropeptide S: a transmitter system in the brain regulating fear and anxiety. Neuropharmacology 58: 29-34. https://doi.org/10.1016/j.neuropharm.2009.06.001
    [11] Xu YL, Gall CM, Jackson VR, et al. (2007) Distribution of neuropeptide S receptor mRNA and neurochemical characteristics of neuropeptide S-expressing neurons in the rat brain. J Comp Neurol 500: 84-102. https://doi.org/10.1002/cne.21159
    [12] Leonard SK, Ring RH (2011) Immunohistochemical localization of the neuropeptide S receptor in the rat central nervous system. Neuroscience 172: 153-163. https://doi.org/10.1016/j.neuroscience.2010.10.020
    [13] Nauta WJ (1958) Hippocampal projections and related neural pathways to the midbrainin the cat. Brain 81: 319-340. https://link.springer.com/chapter/10.1007/978-1-4684-7920-1_9
    [14] Nauta WJ, Domesick VB (1982) Neural associations of the limbic system. Dordrecht: Springer 175-206. https://doi.org/10.1007/978-94-011-6302-6_10
    [15] Soudryl Y, Lemogne C, Malinvaud D, et al. (2011) Olfactory system and emotion: common substrates. Eur Ann Otorhinolaryngol Head Neck Dis 128: 18-23. https://doi.org/10.1016/j.anorl.2010.09.007
    [16] Xu YL, Reinscheid RK, Huitron-Resendiz S, et al. (2004) Neuropeptide S: a neuropeptide promoting arousal and anxiolytic-like effects. Neuron 43: 487-497. https://doi.org/10.1016/j.neuron.2004.08.005
    [17] Clark SD, Duangdao DM, Schulz S, et al. (2011) Anatomical characterization of the neuropeptide S system in the mouse brain by in situ hybridization and immunohistochemistry. J Comp Neurol 519: 1867-1893. https://doi.org/10.1002/cne.22606
    [18] Si W, Aluisio L, Okamura N, et al. (2010) Neuropeptide S stimulates dopaminergic neurotransmission in the medial prefrontal cortex. J Neurochem 115: 475-482. https://doi.org/10.1111/j.1471-4159.2010.06947.x
    [19] Mochizuki T, Kim J, Sasaki K (2010) Microinjection of neuropeptide S into the rat ventral tegmental area induces hyperactivity and increases extracellular levels of dopamine metabolites in the nucleus accumbens shell. Peptides 31: 926-931. https://doi.org/10.1016/j.peptides.2010.02.006
    [20] Raiteri L, Luccini E, Romei C, et al. (2009) Neuropeptide S selectively inhibits the release of 5-HT and noradrenaline from mouse frontal cortex nerve endings. Br J Pharmacol 157: 474-481. https://doi.org/10.1111/j.1476-5381.2009.00163.x
    [21] Pałasz A, Rojczyk E (2015) Neuroleptics affect neuropeptide S and NPSR mRNA levels in the rat brain. J Mol Neurosci 57: 352-357. https://doi.org/10.1007/s12031-015-0625-3
    [22] Gołyszny M, Obuchowicz E (2019) Are neuropeptides relevant for the mechanism of action of SSRIs?. Neuropeptides 75: 1-17. https://doi.org/10.1016/j.npep.2019.02.002
    [23] Laux G (2021) Serotonin Reuptake Inhibitors: Citalopram, Escitalopram, Fluoxetine, Fluvoxamine, Paroxetine, and Sertraline. NeuroPsychopharmacotherapy. Cham.: Springer 1-13. https://doi.org/10.1007/978-3-319-56015-1_413-1
    [24] Feng RF, Ma R, Wang P, et al. (2022) Efficacy of escitalopram for poststroke depression: a systematic review and meta-analysis. Sci Rep 12: 1-10. https://doi.org/10.1038/s41598-022-05560-w
    [25] Zhong H, Haddjeri N, Sánchez C (2012) Escitalopram, an antidepressant with an allosteric effect at the serotonin transporter—a review of current understanding of its mechanism of action. Psychopharmacology 219: 1-13. https://doi.org/10.1007/s00213-011-2463-5
    [26] Pałasz A, Suszka-Świtek A, Filipczyk Ł, et al. (2016) Escitalopram affects spexin expression in the rat hypothalamus, hippocampus and striatum. Pharmacol Rep 68: 1326-1331. https://doi.org/10.1016/j.pharep.2016.09.002
    [27] Pałasz A, Piwowarczyk-Nowak A, Suszka-Świtek A, et al. (2020) Escitalopram as a modulator of proopiomelanocortin, kisspeptin, Kiss1R and MCHR1 gene expressions in the male rat brain. Mol Biol Rep 47: 8273-8278. https://doi.org/10.1007/s11033-020-05806-8
    [28] Gołyszny M, Zieliński M, Paul-Samojedny M, et al. (2022) Escitalopram alters the hypothalamic OX system but does not affect its up-regulation induced by early-life stress in adult rats. Neurosci Res . Ahead of print. https//doi.org/10.1016/j.neures.2022.02.005
    [29] Stahl SM, Morrissette DA, Faedda G, et al. (2017) Guidelines for the recognition and management of mixed depression. CNS Spectrums 22: 203-219. https://doi.org/10.1017/S1092852917000165
    [30] Roseboom PH, Kalin NH (2000) Neuropharmacology of venlafaxine. DepressAnxiety 12: 20-29. https://doi.org/10.1002/1520-6394(2000)12:1+<20::AID-DA3>3.0.CO;2-M
    [31] Stout SC, Owens MJ, Nemeroff CB (2002) Regulation of corticotropin-releasing factor neuronal systems and hypothalamic-pituitary-adrenal axis activity by stress and chronic antidepressant treatment. J Pharmacol Exp Ther 300: 1085-1092. https://doi.org/10.1124/jpet.300.3.1085
    [32] Petschner P, Juhasz G, Tamasi V, et al. (2016) Chronic venlafaxine treatment fails to alter the levels of galanin system transcripts in normal rats. Neuropeptides 57: 65-70. https://doi.org/10.1016/j.npep.2016.01.010
    [33] Poretti MB, Sawant RS, Rask-Andersen M, et al. (2016) Reduced vasopressin receptors activation mediates the anti-depressant effects of fluoxetine and venlafaxine in bulbectomy model of depression. Psychopharmacology 233: 1077-1086. https://doi.org/10.1007/s00213-015-4187-4
    [34] LeMoult J, Humphreys KL, Tracy A, et al. (2020) Meta-analysis: exposure to early life stress and risk for depression in childhood and adolescence. J Am Acad Child Adolesc Psychiatry 59: 842-855. https://doi.org/10.1016/j.jaac.2019.10.011
    [35] Pervanidou P, Makris G, Chrousos G, et al. (2020) Early life stress and pediatric posttraumatic stress disorder. Brain Sci 10: 169. https://doi.org/10.3390/brainsci10030169
    [36] Arborelius L, Hawks BW, Owens MJ, et al. (2004) Increased responsiveness of presumed 5-HT cells to citalopram in adult rats subjected to prolonged maternal separation relative to brief separation. Psychopharmacology 176: 248-255. https://doi.org/10.1007/s00213-004-1883-x
    [37] Lippmann M, Bress A, Nemeroff CB, et al. (2007) Long-term behavioural and molecular alterations associated with maternal separation in rats. Eur J Neurosci 25: 3091-3098. https://doi.org/10.1111/j.1460-9568.2007.05522.x
    [38] Roque S, Mesquita AR, Palha JA, et al. (2014) The behavioral and immunological impact of maternal separation: a matter of timing. Front BehavNeurosci 8: 192. https://doi.org/10.3389/fnbeh.2014.00192
    [39] Bonapersona V, Joels M, Sarabdjitsingh RA (2018) Effects of early life stress on biochemical indicators of the dopaminergic system: A 3 level meta-analysis of rodent studies. NeurosciBiobehav Rev 95: 1-16. https://doi.org/10.1016/j.neubiorev.2018.09.003
    [40] Bravo JA, Dinan TG, Cryan JF (2014) Early-life stress induces persistent alterations in 5-HT1A receptor and serotonin transporter mRNA expression in the adult rat brain. Front Mol Neurosci 7: 1-9. https://doi.org/10.3389/fnmol.2014.00024
    [41] González-Pardo H, Arias JL, Gómez-Lázaro E, et al. (2020) Sex-specific effects of early life stress on brain mitochondrial function, monoamine levels and neuroinflammation. Brain Sci 10: 447. https://doi.org/10.3390/brainsci10070447
    [42] Nishi M (2020) Effects of early-life stress on the brain and behaviors: implications of early maternal separation in rodents. Int J Mol Sci 21: 7212. https://doi.org/10.3390/ijms21197212
    [43] Miragaia AS, de Oliveira Wertheimer GS, Consoli AC, et al. (2018) Maternal deprivation increases anxiety-and depressive-like behaviors in an age-dependent fashion and reduces neuropeptide Y expression in the amygdala and hippocampus of male and female young adult rats. Front BehavNeurosci 12: 159. https://doi.org/10.3389/fnbeh.2018.00159
    [44] Feng P, Vurbic D, Wu Z, et al. (2007) Brain orexins and wake regulation in rats exposed to maternal deprivation. Brain Res 1154: 163-172. https://doi.org/10.1016/j.brainres.2007.03.077
    [45] Marco EM, Llorente R, López-Gallardo M, et al. (2015) The maternal deprivation animal model revisited. NeurosciBiobehav Rev 51: 151-163. https://doi.org/10.1016/j.neubiorev.2015.01.015
    [46] Bülbül M, Sinen O (2022) The influence of early-life and adulthood stressors on brain neuropeptide-S system. Neuropeptides 92: 102223. https://doi.org/10.1016/j.npep.2021.102223
    [47] Harrison EL, Baune BT (2014) Modulation of early stress-induced neurobiological changes: a review of behavioural and pharmacological interventions in animal models. Transl Psychiatry 4: 390. https://doi.org/10.1038/tp.2014.31
    [48] Botticelli L, Micioni Di Bonaventura E, Ubaldi M, et al. (2021) The Neural Network of Neuropeptide S (NPS): Implications in food intake and gastrointestinal functions. Pharmaceuticals 14: 293. https://doi.org/10.3390/ph14040293
    [49] Gur E, Dremencov E, Lerer B, et al. (1999) Venlafaxine: acute and chronic effects on 5-hydroxytryptamine levels in rat brain in vivo. Eur J Pharmacol 372: 17-24. https://doi.org/10.1016/S0014-2999(99)00164-8
    [50] Dazzi L, Vignone V, Seu E, et al. (2002) Inhibition by venlafaxine of the increase in norepinephrine output in rat prefrontal cortex elicited by acute stress or by the anxiogenic drug FG 7142. J Psychopharmacol 16: 125-131. https://doi.org/10.1177/026988110201600202
    [51] Flandreau EI, Bourke CH, Ressler KJ, et al. (2013) Escitalopram alters gene expression and HPA axis reactivity in rats following chronic overexpression of corticotropin-releasing factor from the central amygdala. Psychoneuroendocrinology 38: 1349-1361. https://doi.org/10.1016/j.psyneuen.2012.11.020
    [52] Mesquita AR, Pêgo JM, Summavielle T, et al. (2007) Neurodevelopment milestone abnormalities in rats exposed to stress in early life. Neuroscience 147: 1022-1033. https://doi.org/10.1016/j.neuroscience.2007.04.007
    [53] Levine S, Huchton DM, Wiener SG, et al. (1991) Time course of the effect of maternal deprivation on the hypothalamic-pituitary-adrenal axis in the infant rat. Dev Psychobiol 24: 547-558. https://doi.org/10.1002/dev.420240803
    [54] Suchecki D, Mozaffarian D, Gross G, et al. (1993) Effects of maternal deprivation on the ACTH stress response in the infant rat. Neuroendocrinology 57: 204-212. https://doi.org/10.1159/000126361
    [55] Lehmann J, Pryce CR, Bettschen D, et al. (1999) The maternal separation paradigm and adult emotionality and cognition in male and female Wistar rats. PharmacolBiochemBehav 64: 705-715. https://doi.org/10.1016/S0091-3057(99)00150-1
    [56] Marcondes FK, Miguel KJ, Melo LL, et al. (2001) Estrous cycle influences the response of female rats in the elevated plus-maze test. PhysiolBehav 74: 435-440. https://doi.org/10.1016/S0031-9384(01)00593-5
    [57] Dimatelis JJ, Vermeulen IM, Bugarith K, et al. (2016) Female rats are resistant to developing the depressive phenotype induced by maternal separation stress. Metab Brain Dis 31: 109-119. https://doi.org/10.1007/s11011-015-9723-8
    [58] Paxinos G, Watson C (2006) The rat brain in stereotaxic coordinates: hard cover edition.Elsevier. https://books.google.pl/books?hl=pl&lr=&id=0prYfdDbh58C&oi=fnd&pg=PP1&dq=Paxinos+G,+Watson+C.+The+rat+brain+in+stereotaxic+coordinates:+hard+cover+edition.+Elsevier.+2006.&ots=-9hrEYXGxj&sig=NOP1J-I81ZXmlNrTabF7eFjhEVM&redir_esc=y#v=onepage&q=Paxinos%20G%2C%20Watson%20C.%20The%20rat%20brain%20in%20stereotaxic%20coordinates%3A%20hard%20cover%20edition.%20Elsevier.%202006.&f=false
    [59] Chomczynski P, Sacchi N (1987) Single-step method of RNA isolation by acid guanidinium thiocyanate-phenol-chloroform extraction. Anal Biochem 162: 156-159. https://doi.org/10.1016/0003-2697(87)90021-2
    [60] Livak KJ, Schmittgen TD (2001) Analysis of relative gene expression data using real-time quantitative PCR and the 2− ΔΔCT method. Methods 25: 402-408. https://doi.org/10.1006/meth.2001.1262
    [61] Bondar NP, Merkulova TI (2016) Brain-derived neurotrophic factor and early-life stress: multifaceted interplay. J Biosci 41: 751-758. https://doi.org/10.1007/s12038-016-9648-3
    [62] Alviña K, JodeiriFarshbaf M, Mondal AK (2021) Long term effects of stress on hippocampal function: emphasis on early life stress paradigms and potential involvement of neuropeptide Y. J Neurosci Res 99: 57-66. https://doi.org/10.1002/jnr.24614
    [63] Yam KY, Ruigrok SR, Ziko I, et al. (2017) Ghrelin and hypothalamic NPY/AgRP expression in mice are affected by chronic early-life stress exposure in a sex-specific manner. Psychoneuroendocrinology 86: 73-77. https://doi.org/10.1016/j.psyneuen.2017.09.006
    [64] Guerrini R, Salvadori S, Rizzi A, et al. (2010) Neurobiology, pharmacology, and medicinal chemistry of neuropeptide S and its receptor. Med Res Rev 30: 751-777. https://doi.org/10.1002/med.20180
    [65] Okamura N, Reinscheid RK (2007) Neuropeptide S: a novel modulator of stress and arousal. Stress 10: 221-226. https://doi.org/10.1080/10253890701248673
    [66] Chauveau F, Claverie D, Lardant E, et al. (2020) Neuropeptide S promotes wakefulness through the inhibition of sleep-promoting ventrolateral preoptic nucleus neurons. Sleep 43: zsz189. https://doi.org/10.1093/sleep/zsz189
    [67] Ionescu IA, Dine J, Yen YC, et al. (2012) Intranasally administered neuropeptide S (NPS) exerts anxiolytic effects following internalization into NPS receptor-expressing neurons. Neuropsychopharmacology 37: 1323-1337. https://doi.org/10.1038/npp.2011.317
    [68] Lukas M, Bredewold R, Neumann ID, et al. (2010) Maternal separation interferes with developmental changes in brain vasopressin and oxytocin receptor binding in male rats. Neuropharmacology 58: 78-87. https://doi.org/10.1016/j.neuropharm.2009.06.020
    [69] Nauta WJ, Domesick VB (1978) Crossroads of limbic and striatal circuitry: hypothalamo-nigral connections. [In] Limbic mechanisms. Boston, MA.: Springer 75-93. https://doi.org/10.1007/978-1-4757-0716-8_6
    [70] Daniels WMU, Pietersen CY, Carstens ME, et al. (2004) Maternal separation in rats leads to anxiety-like behavior and a blunted ACTH response and altered neurotransmitter levels in response to a subsequent stressor. Metab Brain Dis 19: 3-14. https://doi.org/10.1023/B:MEBR.000027412.19664.b3
    [71] Valentino RJ, Van Bockstaele E (2001) Opposing regulation of the locus coeruleus by corticotropin-releasing factor and opioids. Psychopharmacology 158: 331-342. https://doi.org/10.1007/s002130000673
    [72] Valentino RJ, Van Bockstaele E (2008) Convergent regulation of locus coeruleus activity as an adaptive response to stress. Eur J Pharmacol 583: 194-203. https://doi.org/10.1016/j.ejphar.2007.11.062
    [73] Valentino RJ, Foote SL, Page ME (1993) The locus coeruleus as a site for integrating corticotropin-releasing factor and noradrenergic mediation of stress responses. An NY Acad Sci 697: 173-188. https://doi.org/10.1111/j.1749-6632.1993.tb49931.x
    [74] Chang S, Deussing JM (2021) Corticotropin-Releasing Hormone in the Paraventricular Nucleus of the Hypothalamus—Beyond Hypothalamic–Pituitary–Adrenal Axis Control. [In] Neuroanatomy of Neuroendocrine Systems. Cham.: Springer 231-250. https://doi.org/10.1007/978-3-030-86630-3_9
    [75] Jüngling K, Liu X, Lesting J, et al. (2012) Activation of neuropeptide S-expressing neurons in the locus coeruleus by corticotropin-releasing factor. J Physiol 590: 3701-3717. https://doi.org/10.1113/jphysiol.2011.226423
    [76] Ross JA, Van Bockstaele EJ (2021) The locus coeruleus-norepinephrine system in stress and arousal: unraveling historical, current, and future perspectives. Front Psychiatry 11: 1581. https://doi.org/10.3389/fpsyt.2020.601519
    [77] Liu D, Caldji C, Sharma S, et al. (2000) Influence of neonatal rearing conditions on stress-induced adrenocorticotropin responses and norepinepherine release in the hypothalamic paraventricular nucleus. J Neuroendocrinol 12: 5-12. https://doi.org/10.1046/j.1365-2826.2000.00422.x
    [78] Matthews K, Dalley JW, Matthews C, et al. (2001) Periodic maternal separation of neonatal rats produces region-and gender-specific effects on biogenic amine content in postmortem adult brain. Synapse 40: 1-10. https://doi.org/10.1002/1098-2396(200104)40:1<1::AID-SYN1020>3.0.CO;2-E
    [79] Bhatnagar S, Vining C, Denski KAI (2004) Regulation of chronic stress-induced changes in hypothalamic-pituitary-adrenal activity by the basolateral amygdala. Ann NY Acad Sci 1032: 315-319. https://doi.org/10.1196/annals.1314.050
    [80] LeDoux J (2007) The amygdala. Curr Biol 17: 868-874. https://europepmc.org/article/med/17956742
    [81] Keshavarzi S, Sullivan RK, Ianno DJ, et al. (2014) Functional properties and projections of neurons in the medial amygdala. J Neurosci 34: 8699-8715. https://doi.org/10.1523/JNEUROSCI.1176-14.2014
    [82] Grund T, Neumann ID (2018) Neuropeptide S induces acute anxiolysis by phospholipase C-dependent signaling within the medial amygdala. Neuropsychopharmacology 43: 1156-1163. https://doi.org/10.1038/npp.2017.169
    [83] Plotsky PM, Owens MJ, Nemeroff CB (1998) Psychoneuroendocrinology of depression: hypothalamic-pituitary-adrenal axis. Psychiatr Clin N Am 21: 293-307. https://doi.org/10.1016/S0193-953X(05)70006-X
    [84] Corradi PF, Corradi RB, Greene LW (2016) Physiology of the hypothalamic pituitary gonadal axis in the male. Urol Clin 43: 151-162. https://doi.org/10.1016/j.ucl.2016.01.001
    [85] Ortiga-Carvalho TM, Chiamolera MI, Pazos-Moura CC, et al. (2011) Hypothalamus-pituitary-thyroid axis. ComprPhysiol 6: 1387-1428. https://doi.org/10.1002/cphy.c150027
    [86] Veenema AH, Blume A, Niederle D, et al. (2006) Effects of early life stress on adult male aggression and hypothalamic vasopressin and serotonin. Eur J Neurosci 24: 1711-1720. https://doi.org/10.1111/j.1460-9568.2006.05045.x
    [87] Veenema AH, Neumann ID (2009) Maternal separation enhances offensive play-fighting, basal corticosterone and hypothalamic vasopressin mRNA expression in juvenile male rats. Psychoneuroendocrinology 34: 463-467. https://doi.org/10.1016/j.psyneuen.2008.10.017
    [88] Lukas M, Neumann ID (2012) Nasal application of neuropeptide S reduces anxiety and prolongs memory in rats: social versus non-social effects. Neuropharmacology 62: 398-405. https://doi.org/10.1016/j.neuropharm.2011.08.016
    [89] VanBodegom M, Homberg JR, Henckens MJ (2017) Modulation of the hypothalamic-pituitary-adrenal axis by early life stress exposure. Front Cell Neurosci 11: 87. https://doi.org/10.3389/fncel.2017.00087
    [90] Bombail V (2019) Perception and emotions: on the relationships between stress and olfaction. Appl BehavAnim Sci 212: 98-108. https://doi.org/10.1016/j.applanim.2018.12.013
    [91] Mikrouli E, Wörtwein G, Soylu R, et al. (2011) Increased numbers of orexin/hypocretin neurons in a genetic rat depression model. Neuropeptides 45: 401-406. https://doi.org/10.1016/j.npep.2011.07.010
    [92] Albert PR, Vahid-Ansari F (2019) The 5-HT1A receptor: signaling to behavior. Biochimie 161: 34-45. https://doi.org/10.1016/j.biochi.2018.10.015
    [93] Gilbert F, Brazell C, Tricklebank MD, et al. (1988) Activation of the 5-HT1A receptor subtype increases rat plasma ACTH concentration. Eur J Pharmacol 147: 431-439. https://doi.org/10.1016/0014-2999(88)90178-1
    [94] Fletcher A, Forster EA, Bill DJ, et al. (1995) Electrophysiological, biochemical, neurohormonal and behavioural studies with WAY-100635, a potent, selective and silent 5-HT1A receptor antagonist. Behav Brain Res 73: 337-353. https://doi.org/10.1016/0166-4328(96)00118-0
    [95] Valentino RJ, Foote SL, Aston-Jones G (1983) Corticotropin-releasing factor activates noradrenergic neurons of the locus coeruleus. Brain Res 270: 363-367. https://doi.org/10.1016/0006-8993(83)90615-7
    [96] Pickel VM, Joh TH, Reis DJ (1977) A serotonergic innervation of noradrenergic neurons in nucleus locus coeruleus: demonstration by immunocytochemical localization of the transmitter specific enzymes tyrosine and tryptophan hydroxylase. Brain Res 131: 197-214. https://doi.org/10.1016/0006-8993(77)90515-7
    [97] Steinbusch HWM (1984) Serotonin-immunoreactive neurons and their projections in the CNS. Handbook of Chemical Neuroanatomy, Chemical Transmitter Receptors in the CNS, 3, Part II : 68-118. https://cir.nii.ac.jp/crid/1572824499186806784
    [98] Leysen JE (2004) 5-HT2 receptors. CurrDrug Targets 3: 11-26. https://doi.org/10.2174/1568007043482598
    [99] Rossi DV, Burke TF, Hensler JG (2008) Differential regulation of serotonin-1A receptor-stimulated [35S] GTPγS binding in the dorsal raphe nucleus by citalopram and escitalopram. Eur J Pharmacol 583: 103-107. https://doi.org/10.1016/j.ejphar.2008.01.022
    [100] Segal M (1979) Serotonergic innervation of the locus coeruleus from the dorsal raphe and its action on responses to noxious stimuli. J Physiol 286: 401-415. https://doi.org/10.1113/jphysiol.1979.sp012628
    [101] Van Bockstaele EJ (2000) Multiple substrates for serotonergic modulation of rat locus coeruleus neurons and relationships with kainate receptors. Brain Res Bull 51: 433-442. https://doi.org/10.1016/S0361-9230(99)00267-1
    [102] West CH, Ritchie JC, Boss-Williams KA, et al. (2009) Antidepressant drugs with differing pharmacological actions decrease activity of locus coeruleus neurons. Int J Neuropsychopharmacol 12: 627-641. https://doi.org/10.1017/S1461145708009474
    [103] Bobker DH, Williams JT (1989) Serotonin agonists inhibit synaptic potentials in the rat locus ceruleus in vitro via 5-hydroxytryptamine1A and 5-hydroxytryptamine1B receptors. J Pharmacol Exp Ther 250: 37-43. https://europepmc.org/article/med/2526217
    [104] Holanda VA, Oliveira MC, Souza LS, et al. (2019) Dopamine D1 and D2 receptors mediate neuropeptide S-induced antinociception in the mouse formalin test. Eur J Pharmacol 859: 172557. https://doi.org/10.1016/j.ejphar.2019.172557
    [105] Nitz D, Siegel J (1997) GABA release in the dorsal raphe nucleus: role in the control of REM sleep. Am J PhysiolRegulIntegr Comp Physiol 273: 451-455. https://doi.org/10.1152/ajpregu.1997.273.1.R451
    [106] Soya S, Sakurai T (2020) Orexin as a modulator of fear-related behavior: hypothalamic control of noradrenaline circuit. Brain Res 1731: 146037. https://doi.org/10.1016/j.brainres.2018.11.032
    [107] Tobinski AM, Rappeneau V (2021) Role of the Neuropeptide S System in Emotionality, Stress Responsiveness and Addiction-Like Behaviours in Rodents: Relevance to Stress-Related Disorders. Pharmaceuticals 14: 780. https://doi.org/10.3390/ph14080780
    [108] Tillage RP, Foster SL, Lustberg D, et al. (2021) Co-released norepinephrine and galanin act on different timescales to promote stress-induced anxiety-like behavior. Neuropsychopharmacology 46: 1535-1543. https://doi.org/10.1038/s41386-021-01011-8
    [109] Millan MJ, Dekeyne A, Papp M, et al. (2001) S33005, a novel ligand at both serotonin and norepinephrine transporters: II. Behavioral profile in comparison with venlafaxine, reboxetine, citalopram, and clomipramine. J Pharmacol Exp Ther 298: 581-591. https://jpet.aspetjournals.org/content/298/2/565.short
    [110] Rossi DV, Valdez M, Gould GG, et al. (2006) Chronic administration of venlafaxine fails to attenuate 5-HT1A receptor function at the level of receptor-G protein interaction. Int J Neuropsychopharmacol 9: 393-406. https://doi.org/10.1017/S1461145705005754
    [111] Béïque JC, Blier P, de Montigny C, et al. (2000) Potentiation by (-) pindolol of the activation of postsynaptic 5-HT1A receptors induced by venlafaxine. Neuropsychopharmacology 23: 294-306. https://doi.org/10.1016/S0893-133X(00)00112-3
    [112] Niimi M (2006) Centrally administered neuropeptide S activates orexin-containing neurons in the hypothalamus and stimulates feeding in rats. Endocrine 30: 75-79. https://doi.org/10.1385/ENDO:30:1:75
    [113] Cannella N, Kallupi M, Ruggeri B, et al. (2013) The role of the neuropeptide S system in addiction: focus on its interaction with the CRF and hypocretin/orexin neurotransmission. Prog Neurobiol 100: 48-59. https://doi.org/10.1016/j.pneurobio.2012.09.005
    [114] Berlau DJ, McGaugh JL (2006) Enhancement of extinction memory consolidation: the role of the noradrenergic and GABAergic systems within the basolateral amygdala. Neurobiol Learn Mem 86: 123-132. https://doi.org/10.1016/j.nlm.2005.12.008
    [115] Roozendaal B, Castello NA, Vedana G, et al. (2008) Noradrenergic activation of the basolateral amygdala modulates consolidation of object recognition memory. Neurobiol Learn Mem 90: 576-579. https://doi.org/10.1016/j.nlm.2008.06.010
    [116] Han RW, Xu HJ, Wang P, et al. (2014) Neuropeptide S interacts with the basolateral amygdala noradrenergic system in facilitating object recognition memory consolidation. Neurobiol Learn Mem 107: 32-36. https://doi.org/10.1016/j.nlm.2013.10.010
    [117] Guarnieri LO, Pereira-Caixeta AR, Medeiros DC, et al. (2020) Pro-neurogenic effect of fluoxetine in the olfactory bulb is concomitant to improvements in social memory and depressive-like behavior of socially isolated mice. Transl Psychiatry 10: 1-14. https://doi.org/10.1038/s41398-020-0701-5
    [118] Zhang J, Dennis KA, Darling RD, et al. (2013) Neonatal citalopram exposure decreases serotonergic fiber density in the olfactory bulb of male but not female adult rats. Front Cell Neurosci 7: 67. https://doi.org/10.3389/fncel.2013.00067
    [119] Thase ME, Shelton RC, Khan A (2006) Treatment with venlafaxine extended release after SSRI nonresponse or intolerance: a randomized comparison of standard-and higher-dosing strategies. J Clin Psychopharmacol 26: 250-258. https://doi.org/10.1097/01.jcp.0000219922.19305.08
    [120] Engelmann J, Wagner S, Solheid A, et al. (2021) Tolerability of high-dose venlafaxine after switch from escitalopram in nonresponding patients with major depressive disorder. J Clin Psychopharmacol 41: 62-66. https://doi.org/10.1097/JCP.0000000000001312
    [121] Bonapersona V, Kentrop J, Van Lissa CJ, et al. (2019) The behavioral phenotype of early life adversity: A 3-level meta-analysis of rodent studies. NeurosciBiobehav Rev 102: 299-307.
    [122] Bonapersona V, Hoijtink H, Sarabdjitsingh RA, et al. (2021) Increasing the statistical power of animal experiments with historical control data. Nat Neurosci 24: 470-477. https://doi.org/10.1038/s41593-020-00792-3
    [123] Button KS, Ioannidis J, Mokrysz C, et al. (2013) Power failure: why small sample size undermines the reliability of neuroscience. Nat Rev Neurosci 14: 365-376. https://doi.org/10.1038/nrn3475
  • neurosci-09-03-022-s001.pdf
  • This article has been cited by:

    1. Dong Qiu, Chengcheng Wang, Jialiang Xie, A novel TODIM-based multi-attribute decision making method under information described by Z-numbers for selecting online B&B, 2024, 663, 00200255, 120315, 10.1016/j.ins.2024.120315
    2. Sijia Zhu, Zhe Liu, Distance measures of picture fuzzy sets and interval-valued picture fuzzy sets with their applications, 2023, 8, 2473-6988, 29817, 10.3934/math.20231525
    3. Huchang Liao, Fan Liu, Yue Xiao, Zheng Wu, Edmundas Kazimieras Zavadskas, A survey on Z-number-based decision analysis methods and applications: What’s going on and how to go further?, 2024, 663, 00200255, 120234, 10.1016/j.ins.2024.120234
  • Reader Comments
  • © 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(2579) PDF downloads(164) Cited by(5)

Figures and Tables

Figures(8)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog