Student 1 | Student 2 | Student 3 | Student 4 | Student 5 | Student 6 | |
˜M | (0.80,0.09) | (0.30,0.01) | (0.66,0.06) | (0.61,0.23) | (0.43,0.05) | (0.60,0.10) |
˜N | (0.80,0.09) | (0.75,0.21) | (0.45,0.08) | (0.70,0.09) | (0.64,0.03) | (0.50,0.14) |
Several pathological conditions might cause the degradation of the cyclin-dependent kinase inhibitor (CKI) p27 and cell cycle arrest at the G1 phase, including cancers and infections. Chlamydia trachomatis (Ctr), as an obligatory intracellular pathogen, has been found to alter the fate of the cell from different aspects. In this study, we aimed to investigate the effect of Ctr infection on the expression of the important cell cycle regularity protein p27 in mesenchymal stem cells (MSCs).
Isolation of MSCs from healthy human fallopian tube was confirmed by detection of the stemness markers Sox2, Nanog and Oct4 and the surface markers CD44, CD73 and CD90 by Western blotting and fluorescence-activated cell sorting analysis. The expression of p27 was downregulated at the protein level upon Ctr D infection measured by Real-Time Quantitative Reverse Transcription PCR (qRT-PCR), IF and Western blotting. Recovery of p27 in Ctr D-infected MSCs was achieved by treatment with difluoromethylornithine (DFMO). Ctr D infected MSCs were able to produce colonies in anchorage-independent soft agar assay.
Ctr D infection was able to downregulate the expression of the important cell cycle regulator protein p27, which will be considered a putative candidate for transformation in Ctr D infected MSCs.
Citation: Mohammad A. Abu-Lubad, Wael Al-Zereini, Munir A. Al-Zeer. Deregulation of the cyclin-dependent kinase inhibitor p27 as a putative candidate for transformation in Chlamydia trachomatis infected mesenchymal stem cells[J]. AIMS Microbiology, 2023, 9(1): 131-150. doi: 10.3934/microbiol.2023009
[1] | Jamalud Din, Muhammad Shabir, Nasser Aedh Alreshidi, Elsayed Tag-eldin . Optimistic multigranulation roughness of a fuzzy set based on soft binary relations over dual universes and its application. AIMS Mathematics, 2023, 8(5): 10303-10328. doi: 10.3934/math.2023522 |
[2] | Rukchart Prasertpong . Roughness of soft sets and fuzzy sets in semigroups based on set-valued picture hesitant fuzzy relations. AIMS Mathematics, 2022, 7(2): 2891-2928. doi: 10.3934/math.2022160 |
[3] | Ahmad Bin Azim, Ahmad ALoqaily, Asad Ali, Sumbal Ali, Nabil Mlaiki, Fawad Hussain . q-Spherical fuzzy rough sets and their usage in multi-attribute decision-making problems. AIMS Mathematics, 2023, 8(4): 8210-8248. doi: 10.3934/math.2023415 |
[4] | R. Mareay, Radwan Abu-Gdairi, M. Badr . Soft rough fuzzy sets based on covering. AIMS Mathematics, 2024, 9(5): 11180-11193. doi: 10.3934/math.2024548 |
[5] | Jia-Bao Liu, Rashad Ismail, Muhammad Kamran, Esmail Hassan Abdullatif Al-Sabri, Shahzaib Ashraf, Ismail Naci Cangul . An optimization strategy with SV-neutrosophic quaternion information and probabilistic hesitant fuzzy rough Einstein aggregation operator. AIMS Mathematics, 2023, 8(9): 20612-20653. doi: 10.3934/math.20231051 |
[6] | Amal T. Abushaaban, O. A. Embaby, Abdelfattah A. El-Atik . Modern classes of fuzzy α-covering via rough sets over two distinct finite sets. AIMS Mathematics, 2025, 10(2): 2131-2162. doi: 10.3934/math.2025100 |
[7] | Muhammad Naeem, Muhammad Qiyas, Lazim Abdullah, Neelam Khan, Salman Khan . Spherical fuzzy rough Hamacher aggregation operators and their application in decision making problem. AIMS Mathematics, 2023, 8(7): 17112-17141. doi: 10.3934/math.2023874 |
[8] | D. Jeni Seles Martina, G. Deepa . Some algebraic properties on rough neutrosophic matrix and its application to multi-criteria decision-making. AIMS Mathematics, 2023, 8(10): 24132-24152. doi: 10.3934/math.20231230 |
[9] | 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 |
[10] | Mona Hosny . Generalization of rough sets using maximal right neighborhood systems and ideals with medical applications. AIMS Mathematics, 2022, 7(7): 13104-13138. doi: 10.3934/math.2022724 |
Several pathological conditions might cause the degradation of the cyclin-dependent kinase inhibitor (CKI) p27 and cell cycle arrest at the G1 phase, including cancers and infections. Chlamydia trachomatis (Ctr), as an obligatory intracellular pathogen, has been found to alter the fate of the cell from different aspects. In this study, we aimed to investigate the effect of Ctr infection on the expression of the important cell cycle regularity protein p27 in mesenchymal stem cells (MSCs).
Isolation of MSCs from healthy human fallopian tube was confirmed by detection of the stemness markers Sox2, Nanog and Oct4 and the surface markers CD44, CD73 and CD90 by Western blotting and fluorescence-activated cell sorting analysis. The expression of p27 was downregulated at the protein level upon Ctr D infection measured by Real-Time Quantitative Reverse Transcription PCR (qRT-PCR), IF and Western blotting. Recovery of p27 in Ctr D-infected MSCs was achieved by treatment with difluoromethylornithine (DFMO). Ctr D infected MSCs were able to produce colonies in anchorage-independent soft agar assay.
Ctr D infection was able to downregulate the expression of the important cell cycle regulator protein p27, which will be considered a putative candidate for transformation in Ctr D infected MSCs.
Pawlak first proposed the rough set theory[1], which is the basis for testing the granularity of knowledge[2]. In recent years, many models related to rough sets have emerged, such as the rough set theory based on fuzzy covering[3,4,5]. The fuzzy set theory was first proposed by Zadeh[6]. Since then, theories and applications related to fuzzy sets[7] have also been widely studied, such as fuzzy soft sets[8], feature selection of fuzzy sets[9], outlier detection of fuzzy sets[10,11,12], decision application of fuzzy sets, etc.[13,14,15,16]. The relation and difference between fuzzy set theory and rough set theory is also a hot topic. An important component of this research is the roughness of the fuzzy set. Dubois et al first defined the concepts of the rough fuzzy set and fuzzy rough set[17]. The roughness measurement method of fuzzy sets proposed by Banerjee et al really makes the relationship between fuzzy sets and rough sets closer[18], and it has laid a solid foundation for subsequent researchers to explore the roughness measurement of fuzzy sets by applying fuzzy entropy[19], from the perspective of distance[20] and based on soft relation[21]. Li first mentioned the concept of disturbed fuzzy sets[22]. Liu and Chen formally described the concept of disturbed fuzzy sets[23]. Chen and Wu extended the tautology of fuzzy sets[24] to interval-valued fuzzy sets[25], intuitionistic fuzzy sets[26], and disturb fuzzy sets[27], respectively. It is found that the same result can be obtained only when the disturbation fuzzy set is generalized to the ordinary fuzzy set. Therefore, the disturbation fuzzy set shows excellent properties in the operation and has extensive research value, which is not found in any kind of fuzzy set, including the interval valued fuzzy set. Subsequently, Han et al. put forward the concept of disturbed fuzzy rough sets and the roughness measure of disturbed fuzzy sets[28]. It further enriches the theoretical basis of combining the fuzzy set and the rough set. However, there are few researches on the roughness measurement of the disturbance fuzzy set, and the application of disturbance fuzzy set roughness measurement is even less.
Upper and lower approximations of fuzzy sets are two important aspects in the study of fuzzy rough sets theory[29]. In this paper, there are two limitations: On the one hand, it is found in the exploration that the approximation of ˜M∪˜N generally cannot be obtained by the approximation of ˜M and ˜N, and these properties are the result of logical forms defined by assumptions in the domain of discussion expressed in an approximate manner[30]. Therefore they bring inconvenience and difficulty to the research in many fields, including the roughness measurement of disturbed fuzzy sets. On the other hand, when data analysis, data mining, decision support system, and machine learning are carried out, the datasets are usually huge, in order to solve the inconvenience caused by too large datasets. So in this paper, first, the related concepts of the rough set, disturbation fuzzy set, and roughness measurement are introduced. Second, by introducing two new operators designed by Zhang et al. and associating them with the disturbation fuzzy set, the limitation that the execution subset is not the equality of the set and cannot be studied quantitatively is effectively solved. Finally, the roughness measure of the disturbation fuzzy set is studied quantitatively, and its boundedness is obtained. Therefore, it is expected that using the boundary of roughness measure of the disturbing fuzzy set proved in this paper can effectively avoid the computing space outside the boundary and improve the computing efficiency.
In this section, some basic concepts related to approximate space, upper and lower approximations of fuzzy sets, the roughness measure of fuzzy sets, and disturbation fuzzy sets are given.
Definition 2.1 (Approximate space)[1] The nonempty set U is called the discourse domain, S is the equivalence relation on U, and (U,S) is called an approximate space.
Definition 2.2 (Upper approximation, lower approximation, and boundary field)[1] (U,S) is the known approximation space, M⊆U, and in the approximation space y1,y2,⋯,yk represents an equivalence class with respect to S. ˉS(M) is the upper approximation of M and S_(M) is the lower approximation of M. The boundary area BNS is represented by
S_(M)={yi|[yi]S⊆M},S(M)={yi|[yi]S∩M≠∅}, | (2.1) |
while
BNS=ˉS(M)s_(M),k=1,2,⋯,m. |
Definition 2.3. (Upper and lower approximations of fuzzy sets) [1] In U, the upper and lower approximations of the fuzzy set M are defined as: U/S→[0,1] and
S_(M)(y)=infy∈YkM(x), |
ˉS(M)(y)=supy∈YkM(x),k=1,2,⋯,m. |
Definition 2.4. (Roughness measure of fuzzy set)[1] (U,S) is the known approximation space, M⊆U, and the M roughness measure in (U,S) is
ρM=1−|s_(M)||ˉS(M)|, |
where the set |∗| represents the cardinality of ∗.
Yao[2] once proposed that the roughness measure of a fuzzy set can be understood as the distance between the upper approximation and the lower approximation of the fuzzy set. If M: U→[0,1] is in U, M(y),y∈U gives y membership in M.
Definition 2.5. (Disturbed fuzzy sets)[23] If
˜P:Z↦ω,z↦˜P(z) | (2.2) |
and
ω={˜P(z)=(˜Pα(z),˜Pβ(z))|˜Pα(z),˜Pβ(z)∈[0,1]} | (2.3) |
call ˜P a disturbed fuzzy set on Z, then all disturbed fuzzy sets on the discourse domain U are denoted as ˜E(U).
Based on the concepts of upper approximation and lower approximation, this section introduces the roughness measure formula of the disturbed fuzzy set, the operation relations of upper approximation, and lower approximation, and the key properties of roughness measure of the disturbed fuzzy set.
Definition 3.1. (Operation of disturbed fuzzy sets)[28] Let
ω={μ=(μα,μβ)}, |
the interval corresponding to (μα,μβ) is
[max(0,μα−μβ),min(1,μα+μβ)] | (3.1) |
for all
μ=(μα,μβ),ν=(να,νβ),μ,ν∈ω, |
the operation on ω is defined as
μ∧ν=(min{μα,να},max{μβ,νβ}),μ∨ν=(max{μα,να},min{μβ,νβ}),μc=(1−μα,1−μβ). | (3.2) |
Definition 3.2. (Relation of disturbed fuzzy sets)[28] The relationship between μ and ν is defined as
μ=ν⇔μα=να,μβ=νβ,μ≤ν⇔μα≤να,μβ≥νβ,μ<ν⇔μα<να,μβ≥νβ or μα≤να,μβ<νβ, | (3.3) |
otherwise, we call it incomparable and denote by U(μ,ν).
Obviously, when (ω,≤), ¯0=(0,1) and ¯1=(1,0) are the minimum and maximum elements on ω, respectively.
Definition 3.3. (Upper and lower approximations of disturbed fuzzy sets)[28] Let μ,ν be the two given parameters,
˜M∈˜E(U),˜0<ν≤μ≤˜1, |
and the (U,S) be the approximate space, defining the upper and lower approximations of a disturbed fuzzy set. The μ− cut sets and ν− cut sets of S_(˜M) and ˉS(˜M) are
(S_(˜M))μ={y∈U|(˜M)(y)≥μ}, | (3.4) |
(ˉS(˜M))ν={y∈U|ˉS(˜M)(y)≥ν}, | (3.5) |
where, (S_(˜M))μ and (ˉS(˜M))ν can be regarded as the sets of objects with μ and ν as the minimum membership degrees in the disturbance fuzzy set ˜M.
Definition 3.4. (Roughness of disturbed fuzzy set)[28] Let (U,S) be the approximate space,
˜M∈˜E(U),ˉ0<ν≤μ≤ˉ1, |
then the roughness of the disturbed fuzzy set ˜M on U in accordance with parameter μ,ν is
˜ρ˜μ,˜ν˜M=1−|S_(˜M)˜μ||ˉS(˜M)˜ν|. | (3.6) |
Han et al. introduced several key properties of this roughness measure[28].
Proposition 3.1. (Disturbation of upper and lower approximation of fuzzy sets)[28] Let μ,ν be two given parameters,
˜M∈˜E(U),0<ν≤μ≤1, |
and let (S_(˜M))μ and (ˉS(˜M))ν be the μ− cut sets and ν− cut sets of the upper and lower approximations of the disturbed fuzzy set S_(˜M) and ˉS(˜M), where
(ˉS(˜M∪˜N))ν=(ˉS(˜M))ν∪(ˉS(˜N))ν, | (3.7) |
(S_(˜M∩˜N))μ=(S_(˜M))μ∩(S_(˜N))μ, | (3.8) |
(S_(˜M))μ∪(S_(˜N))μ⊆(S_(˜M∪˜N))μ, | (3.9) |
(ˉS(˜M∩˜N))ν⊆(ˉS(˜M))ν∩(ˉS(˜N))ν. | (3.10) |
Property 3.1. For disturbed fuzzy set ˜M,˜N, there is[28]
˜ρμ,ν˜M∪˜N=1−|(S_(˜M∪˜N))μ||(ˉS(˜M∪˜N))ν|=1−|(S_(˜M∪˜N))μ||(ˉS(˜M))ν∪(ˉS(˜N))ν|≤1−|(S_(˜M))μ∪(S_(˜N))μ||(ˉS(˜M))ν∪(ˉS(˜N))ν|, | (3.11) |
˜ρμ,ν˜M∩˜N=1−|(S_(˜M∩˜N))μ||(ˉS(˜M∩˜N))ν|=1−|(S_(˜M))μ∩(S_(˜N))μ||(ˉS(˜M∩˜N))ν|≤1−|(S_(˜M))μ∩(S_(˜N))μ||(ˉS(˜M))ν∩(ˉS(˜N))ν|. | (3.12) |
The pioneering study of fuzzy sets[1] derived as (3.8) and (3.9) in Proposition 3.1, which carry out the property that subsets are not equal sets, hindered the quantitative study of fuzzy sets. Because of this difficulty, Zhang et al. designed two new operators[31]. In this section, the new operator proposed by Zhang et al. is fully associated with the disturbed fuzzy set so as to effectively avoid the bad influence of this property in the roughness measurement process of the disturbed fuzzy set. The roughness measure of the disturbed fuzzy set can be studied quantitatively.
Definition 4.1. (Determine the increment operator)[31] Let the discourse domain be U,S, the equivalence class on U, P,Q⊆U, when P is extended by Q(i.e., P∪Q),
X_(⋅)(⋅):U×U→U, |
defining
X_(P)(Q)=∪{[p]S|p∈H(P),hP(p)⊄Q}, |
and lP(p)⊆Q is called the definite increment of P, where
H(P)=∪{hP(p)|p∈BNS(P)∩P}, |
lP(p)=[p]S−PandhP(p)=[p]S−lP(p). |
Definition 4.2. (Uncertain decrement operator)[31] Let the discourse domain be U, S the equivalence class on U, P,Q⊆U, when P is cut by Q(i.e., P∩Q),
X_(⋅)(⋅):U×U→U, |
defining
ˉX(P)(Q)=∪{[p]S|p∈H(P),hP(p)∩Q=∅} |
and
lP(p)∩Q≠∅, |
which is called the uncertainty decrement of P, where
H(P)=∪{hP(p)|p∈BNS(P)∩P}, |
lP(p)=[p]S−PandhP(p)=[p]S−lP(p). |
Property 4.1. [31] P,Q⊆U, so
X_(P)(Q)=X_(Q)(P), | (4.1) |
ˉX(P)(Q)=ˉX(Q)(P). | (4.2) |
Property 4.2. [31]
X_(P)(∅)=∅, | (4.3) |
X_(P)(P)=∅, | (4.4) |
X_(P)(¬P)=BNS(P)=ˉSP−S_P. | (4.5) |
Property 4.3. [31]
ˉX(P)(∅)=∅, | (4.6) |
ˉX(P)(P)=∅, | (4.7) |
ˉX(P)(¬P)=BNS(P). | (4.8) |
Theorem 4.1. Let ˜M and ˜N be two disturbed fuzzy sets in the discourse domain U. Parameters μ,ν satisfy 0<ν≤μ≤1, while \underline{X}˜Mμ(˜Nμ), ˉX˜Mν(˜Nν), \underline{X}˜Nμ(˜Mμ), and ˉX˜Nν(˜Mν) are, respectively, ˜Mμ, ˜Nμ determines the increment and ˜Mν, and the uncertainty of ˜Nν decreases so we can get
(S_(˜M∪˜N))μ=(S_(˜M))μ∪(S_(˜N))μ∪X_˜Mμ(˜Nμ)=(S_(˜M))μ∪(S_(˜N))μ∪X_˜Nμ(˜Mμ), | (4.9) |
(ˉS(˜M∩˜N))ν=(ˉS(˜M))ν∩(ˉS(˜N))ν−ˉX˜Mν(˜Nν)=(ˉS(˜M))ν∩(ˉS(˜N))ν−ˉX˜Nν(˜Mν). | (4.10) |
Property 4.4. For disturbed fuzzy sets ˜M and ˜N,
˜ρμ,ν˜M∪˜N=1−|(S_(˜M))μ∪(S_(˜N))μ∪X_˜Mμ(˜Nμ)||(ˉS(˜M))ν∪(ˉS(˜N))ν|=1−|(S_(˜M))μ∪(S_(˜N))μ∪X_˜Nμ(˜Mμ)||(ˉS(˜M))ν∪(ˉS(˜N))ν,|, | (4.11) |
˜ρμ,ν˜M∩˜N=1−|((˜M))μ∩((˜N))μ||(ˉS(˜M))ν∩(ˉS(˜N))ν−ˉX˜Mν(˜Nν)|=1−|((˜M))μ∩((˜N))μ||(ˉS(˜M))ν∩(ˉS(˜N))ν−ˉX˜Nν(˜Mν)|. | (4.12) |
When calculating the roughness measurement of disturbed fuzzy sets, the datasets of many programs are huge and the measurement is very complicated and cumbersome work, which requires a lot of manpower and material resources. Therefore, this section presents the boundaries of some results necessary for the roughness measurement of disturbed fuzzy sets. Understanding the boundaries of these results before operation can greatly improve work efficiency. It has very important practical significance.
Theorem 5.1. The upper bound of the roughness measure ˜ρ˜μ,˜ν˜M∪˜N of the disturbed fuzzy sets ˜M and ˜N in the discourse domain U is
˜ρ˜μ,˜ν˜M∪˜N≤1−˜ρ˜μ,˜ν˜M˜ρ˜μ,˜ν˜N2−(˜ρ˜μ,˜ν˜M+˜ρ˜μ,˜ν˜N) |
with respect to parameter μ,ν, satisfying 0<ν≤μ≤1.
Proof. From (3.7) in Proposition 3.1 and the fundamental properties of sets, we can get
˜ρ˜μ,˜ν˜M∪˜N≤1−max{|(S_(˜M))μ|,|(S_(˜N))μ|}|(ˉS(˜M))ν|+|(ˉS(˜N))ν|, | (5.1) |
if
|(S_(˜M))μ|≥|(S_(˜N))μ|. |
Thus
˜ρ˜μ,˜ν˜M∪˜N≤1−1(|(ˉS(˜M))ν||(s_(˜M))μ|+||(ˉS(˜N))ν|||(s_(˜M))μ|), | (5.2) |
so, by Definition 3.4, we get
˜ρ˜μ,˜ν˜M∪˜N≤1−˜ρ˜μ,˜ν˜M˜ρ˜μ,˜ν˜N2−(˜ρ˜μ,˜ν˜M+˜ρ˜μ,˜ν˜N). | (5.3) |
Theorem 5.2. The upper bound of the roughness measure ˜ρ˜μ,˜ν˜M∪˜N of the disturbed fuzzy sets ˜M and ˜N in the discourse domain U is
˜ρ˜μ,˜ν˜M∩˜N≤˜ρ˜μ,˜ν˜M+˜ρ˜μ,˜ν˜N−1+U∘ |
with respect to parameter μ,ν, satisfying 0<ν≤μ≤1 and
U∘=|(s_(˜M∪˜N))μ||(ˉS(˜M∩˜N))ν|. |
Proof. From (3.8) in Proposition 3.1 and the fundamental properties of sets, we can get
˜ρ˜μ,˜ν˜M∩˜N=1−|(S_(˜M))μ||(ˉS(˜M∩˜N))ν|−|(S_(˜N))μ||(ˉS(˜M∩˜N))ν|+|(S_(˜M∪˜N))μ||(ˉS(˜M∩˜N))ν|. | (5.4) |
Also, according to (3.10) in Proposition 3.1,
(ˉS(˜M∩˜N))ν⊆(ˉS(˜M))ν, | (5.5) |
(ˉS(˜M∩˜N))ν⊆(ˉS(˜N))ν. | (5.6) |
In other words, we have
|(ˉS(˜M∩˜N))ν|⊆|(ˉS(˜M))ν|, | (5.7) |
|(ˉS(˜M∩˜N))ν|⊆|(ˉS(˜N))ν|, | (5.8) |
so we can get
|(S_(˜M))μ||(ˉS(˜M))ν|≤|((S_˜M))μ||(ˉS(˜M∩˜N))ν|, | (5.9) |
|(S_(˜N))μ||(ˉS(˜N))ν|≤|(S_(˜N))μ||(ˉS(˜M∩˜N))ν|. | (5.10) |
Next, according to (3.9) in Proposition 3.1, it is obtained
˜ρ˜μ,˜ν˜M∩˜N≤1−|(S_(˜M))μ||(ˉS(˜M))ν|−|(S_(˜N))μ||(ˉS(˜N))ν|+|(S_(˜M∪˜N))μ||(ˉS(˜M∩˜N))ν|. | (5.11) |
According to Definition 3.4, we can get
˜ρ˜μ,˜ν˜M∩˜N≤˜ρ˜μ,˜ν˜M+˜ρ˜μ,˜ν˜N−1+|(S_(˜M∪˜N))μ||(ˉS(˜M∩˜N))ν|. | (5.12) |
Therefore, to sum up,
˜ρ˜μ,˜ν˜M∩˜N≤˜ρ˜μ,˜ν˜M+˜ρ˜μ,˜ν˜N−1+U∘, |
when
U∘=|(s_(˜M∪˜N))μ||(ˉS(˜M∩˜N))ν|. |
Remark 5.1. The bounds of Theorem 5.1 depend on roughness measures of the disturbed fuzzy sets ˜M and ˜N, and the bounds of Theorem 5.2 depend on roughness measures of the disturbed fuzzy sets ˜M and ˜N as well as (S_(˜M∪˜N))μ and (ˉS(˜M∩˜N))ν.
Theorem 5.3. The lower bound of the disturbed fuzzy sets ˜M and ˜N in the discourse domain U for the roughness measure ˜ρ˜μ,˜ν˜M∪˜N with respect to parameter μ,ν is
˜ρ˜μ,˜ν˜M∪˜N≥˜ρ˜μ,˜ν˜M+˜ρ˜μ,˜ν˜N−1+L∘, |
which satisfies 0<ν≤μ≤1, and
L∘=|X_˜Mμ(˜Nμ)|max{|(ˉS(˜M))ν|,|(ˉS(˜N))ν|}. |
Proof. From (4.11) in Property 4.4 and the fundamental properties of sets, it is obtained that
˜ρ˜μ,˜ν˜M∪˜N≥1−|(S_(˜M))μ|+|(S_(˜N))μ|+|X_˜Mμ(˜Nμ)|max{|(ˉS(˜M))ν|,|(ˉS(˜N))ν|}, | (5.13) |
We can obtain
|(ˉS(˜M))v|≥|(ˉS(˜N))ν| | (5.14) |
and
˜ρ˜μ,˜ν˜M∪˜N≥1−|(S_(˜M))μ|+|(S_(˜N))μ|+|X_˜Mμ(˜Nμ)||(ˉS(˜M))ν|=1−|(S_(˜M))μ||(ˉS(˜M))ν|−|(S_(˜N))μ||(ˉS(˜M))ν|−|X_˜Mμ(˜Nμ)||(ˉS(˜M))ν|, | (5.15) |
According to Definition 3.4 and
|(s_(˜N))μ||(ˉS(˜M))ν|≤|(s_(˜N))μ||(ˉS(˜N))ν|, |
we can get
˜ρ˜μ,˜ν˜M∪˜N≥1−|(S_(˜M))μ||(ˉS(˜M))ν|−|(S_(˜N))μ||(ˉS(˜M))ν|−|X_˜Mμ(˜Nμ)||(ˉS(˜M))ν|=1−(1−˜ρ˜μ,˜ν˜M)−(1−˜ρ˜μ,˜ν˜N)−|X_˜Mμ(˜Nμ)||(ˉS(˜M))ν|, | (5.16) |
so
˜ρ˜μ,˜ν˜M∪˜N≥˜ρ˜μ,˜ν˜M+˜ρ˜μ,˜ν˜N−1−|X_˜Mμ(˜Nμ)||(ˉS(˜M))ν|. | (5.17) |
Likewise,
|(ˉS(˜M))v|<|(ˉS(˜N))ν|, | (5.18) |
we can get
˜ρ˜μ,˜ν˜M∪˜N≥1−|(S_(˜M))μ|+|(S_(˜N))μ|+|X_˜Mμ(˜Nμ)||(ˉS(˜N))ν|, | (5.19) |
thus,
˜ρ˜μ,˜ν˜M∪˜N≥˜ρ˜μ,˜ν˜M+˜ρ˜μ,˜ν˜N−1−|X_˜Mμ(˜Nμ)||(ˉS(˜N))ν|. | (5.20) |
To sum up,
˜ρ˜μ,˜ν˜M∪˜N≥˜ρ˜μ,˜ν˜M+˜ρ˜μ,˜ν˜N−1+L∘, |
when
L∘=|X_˜Mμ(˜Nμ)|max{|(ˉS(˜M))ν|,|(ˉS(˜N))ν|}. |
Theorem 5.4. The lower bound of the disturbed fuzzy sets ˜M and ˜N in the discourse domain U for the roughness measure ˜ρ˜μ,˜ν˜M∩˜N with respect to parameter μ,ν is
˜ρ˜μ,˜ν˜M∩˜N≥1−1−˜ρ˜μ,˜ν˜M−˜ρ˜μ,˜ν˜N+˜ρ˜μ,˜ν˜M˜ρ˜μ,˜ν˜N2−˜ρ˜μ,˜ν˜M−˜ρ˜μ,˜ν˜N−I∘(1−˜ρ˜μ,˜ν˜M)(1−˜ρ˜μ,˜ν˜N), |
which satisfies 0<ν≤μ≤1, and
I∘=|(ˉS(˜M∪˜N))ν|+|ˉX˜Mν(˜Nν)|min{|(s_(˜M))μ|,|(s_(˜N))μ|}. |
Proof. From (4.12) in Property 4.4 and the fundamental properties of sets, it is obtained that
˜ρ˜μ,˜ν˜M∩˜N≥1−min{|X_((˜M))μ|,|X_((˜N))μ|}|(ˉS(˜M))ν|+|(ˉS(˜N))ν|−|(ˉS(˜M∪˜N))ν|−|ˉX˜Mν(˜Nν)|, | (5.21) |
if
|(S_(˜M))μ|≤|(S_(˜N))μ|, | (5.22) |
we can get
˜ρ˜μ,˜ν˜M∩˜N≥1−1|(ˉS(˜M))ν||(s_(˜M))μ|+|(ˉS(˜N))ν||(s_(˜M))μ|−|(ˉS(˜M∪˜N))ν||(s_(˜M))μ|−|ˉX˜Mν(˜Nν)||(s_(˜M))μ|. | (5.23) |
According to Definition 3.4 and
|(ˉS(˜N))ν||(s_(˜M))μ|≥|(ˉS(˜N))ν||((s_˜N))μ|, |
we can get
˜ρ˜μ,˜ν˜M∩˜N≥1−1|(ˉS(˜M))ν||(s_(˜M))μ|+|(ˉS(˜N))ν||(s_(˜M))μ|−|(ˉS(˜M∪˜N))ν||(s_(˜M))μ|−|ˉX˜Mν(˜Nν)||(s_(˜M))μ|=1−111−˜ρ˜μ,˜ν˜M+11−˜ρ˜μ,˜ν˜N−|(ˉS(˜M∪˜N))ν|+|ˉX˜Mν(˜Nν)||(s_(˜M))μ|. | (5.24) |
Therefore, define
I|((˜M))μ|=|(ˉS(˜M∪˜N))ν|+|ˉX˜Mν(˜Nν)||(s_(˜M))μ|, | (5.25) |
so
˜ρ˜μ,˜ν˜M∩˜N≥1−1−˜ρ˜μ,˜ν˜M−˜ρ˜μ,˜ν˜N−˜ρ˜μ,˜ν˜M˜ρ˜μ,˜ν˜N2−˜ρ˜μ,˜ν˜M−˜ρ˜μ,˜ν˜N−I|(s_(˜M))μ|(1−˜ρ˜μ,˜ν˜M)(1−˜ρ˜μ,˜ν˜N). | (5.26) |
Likewise, for
|(S_(˜M))μ|>|(S_(˜N))μ|, | (5.27) |
define
I|((˜N))μ|=|(ˉS(˜M∪˜N))ν|+|ˉX˜Mν(˜Nν)||(S_(˜N))μ|, | (5.28) |
so
˜ρ˜μ,˜ν˜M∩˜N≥1−1−˜ρ˜μ,˜ν˜M−˜ρ˜μ,˜ν˜N−˜ρ˜μ,˜ν˜M˜ρ˜μ,˜ν˜N2−˜ρ˜μ,˜ν˜M−˜ρ˜μ,˜ν˜N−I|(s_(˜N))μ|(1−˜ρ˜μ,˜ν˜M)(1−˜ρ˜μ,˜ν˜N). | (5.29) |
Thus, to sum up
˜ρ˜μ,˜ν˜M∩˜N≥1−1−˜ρ˜μ,˜ν˜M−˜ρ˜μ,˜ν˜N+˜ρ˜μ,˜ν˜M˜ρ˜μ,˜ν˜N2−˜ρ˜μ,˜ν˜M−˜ρ˜μ,˜ν˜N−I∘(1−˜ρ˜μ,˜ν˜M)(1−˜ρ˜μ,˜ν˜N), |
when
I∘=|(ˉS(˜M∪˜N))ν|+|ˉX˜Mν(˜Nν)|min{|(s_(˜M))μ|,|(s_(˜N))μ|}. |
Remark 5.2. The lower bound of ˜ρ˜μ,˜ν˜M∩˜N is different from the upper bound of ˜ρ˜μ,˜ν˜M∩˜N, and the roughness measure depends not only on the disturbation fuzzy sets ˜M and ˜N, but also on |(ˉS(˜M))ν|,|(ˉS(˜N))ν|,|(S_(˜M))μ|,|(S_(˜N))μ|, and |ˉX˜Mν(˜Nν)|.
Remark 5.3. In the study of the disturbed fuzzy set, it is fully understood that the roughness measure of the disturbed fuzzy set is bounded, and often roughness comparison can be made by roughly calculating the roughness measure limit of the disturbed fuzzy set, which can greatly reduce the calculation amount.
In the previous section, it has been proved that the roughness measure of perturbed fuzzy sets is bounded, but the bound of the roughness measure of disturbed fuzzy sets can be fully applied in practical problems. Next, the superiority of the theory proposed in this paper is demonstrated more clearly through a practical application of grouping different students in a competition, as shown in Tables 1–5.
Student 1 | Student 2 | Student 3 | Student 4 | Student 5 | Student 6 | |
˜M | (0.80,0.09) | (0.30,0.01) | (0.66,0.06) | (0.61,0.23) | (0.43,0.05) | (0.60,0.10) |
˜N | (0.80,0.09) | (0.75,0.21) | (0.45,0.08) | (0.70,0.09) | (0.64,0.03) | (0.50,0.14) |
Student 1 | Student 2,Student 3,Student 5 | Student 4,Student 6 | |
S_(˜M) | (0.80,0.09) | (0.30,0.06) | (0.60,0.23) |
S_(˜N) | (0.66,0.03) | (0.45,0.21) | (0.50,0.14) |
ˉS(˜N) | (0.66,0.03) | (0.75,0.03) | (0.70,0.09) |
Student 1 | Student 2,Student 3,Student 5 | Student 4,Student 6 | |
S_(˜M∪˜N) | (0.80,0.03) | (0.64,0.06) | (0.60,0.09) |
ˉS(˜M∪˜N) | (0.66,0.09) | (0.75,0.01) | (0.70,0.01) |
S_(˜M∩˜N) | (0.66,0.09) | (0.30,0.21) | (0.50,0.23) |
ˉS(˜M∩˜N) | (0.66,0.09) | (0.45,0.05) | (0.61,0.14) |
Student 1,Student 4 | Student 2,Student 5 | Student 3,Student 6 | |
S_(˜M) | (0.61,0.23) | (0.30,0.05) | (0.60,0.10) |
ˉS(˜M) | (0.80,0.09) | (0.43,0.01) | (0.66,0.06) |
S_(˜N) | (0.66,0.09) | (0.64,0.21) | (0.45,0.14) |
ˉS(˜N) | (0.70,0.03) | (0.75,0.03) | (0.50,0.08) |
Student 1,Student 4 | Student 2,Student 5 | Student 3,Student 6 | |
S_(˜M∪˜N) | (0.70,0.09) | (0.64,0.03) | (0.60,0.10) |
ˉS(˜M∪˜N) | (0.80,0.03) | (0.75,0.01) | (0.66,0.06) |
S_(˜M∩˜N) | (0.61,0.23) | (0.30,0.21) | (0.45,0.14) |
ˉS(˜M∩˜N) | (0.66,0.09) | (0.43,0.05) | (0.50,0.08) |
Example 6.1. Due to receiving the notice that our province will soon hold a student learning competition to test the learning ability of two subjects of mathematics and Chinese, the school will send 6 students to participate in the competition. It is known that each student's ability level assessment of mathematics and Chinese constitutes a disturbance fuzzy set. The school will formulate two combinations, respectively,
A:{{student1},{student2,student3,student5},{student4,student6}}, |
B:{{student1,student4},{student2,student5},{student3,student6}}. |
If you want to know which combination is more likely to win, set parameter
(0.00,0.00)<μ=ν≤(0.60,0.10), |
(in real life, people usually think that 60 is a passing grade on a 100-point scale, and the parameter selection of different practical questions will be different). Table 1 is the assessment table of students' mathematical and language ability levels. The mathematics of disturbed fuzzy sets and the language of disturbed fuzzy sets are represented by ˜M and ˜N, respectively.
So, according to Definition 3.4 and Tables 2 and 4,
˜ρ˜μ,˜ν˜M(A)=1−|S_(˜M)˜μ||ˉS(˜M)˜ν|=1−16=56,˜ρ˜μ,˜ν˜N(A)=1−|S_(˜N)˜μ||ˉS(˜N)˜ν|=1−16=56, | (6.1) |
˜ρ˜μ,˜ν˜M(B)=1−|S_(˜M)˜μ||ˉS(˜M)˜ν|=1−24=12,˜ρ˜μ,˜ν˜N(B)=1−|S_(˜N)˜μ||ˉS(˜N)˜ν|=1−24=12. | (6.2) |
From Theorems 5.1–5.4, it follows
˜ρ˜μ,˜ν˜M∩˜N(A)≤˜ρ˜μ,˜ν˜M+˜ρ˜μ,˜ν˜N−1+U∘=203, | (6.3) |
˜ρ˜μ,˜ν˜M∩˜N(A)≥1−1−˜ρ˜μ,˜ν˜M−˜ρ˜μ,˜ν˜N+˜ρ˜μ,˜ν˜M˜ρ˜μ,˜ν˜N2−˜ρ˜μ,˜ν˜M−˜ρ˜μ,˜ν˜N−I∘(1−˜ρ˜μ,˜ν˜M)(1−˜ρ˜μ,˜ν˜N)=1718, | (6.4) |
˜ρ˜μ,˜ν˜M∩˜N(B)≤˜ρ˜μ,˜ν˜M+˜ρ˜μ,˜ν˜N−1+U∘=3, | (6.5) |
˜ρ˜μ,˜ν˜M∩˜N(B)≥1−1−˜ρ˜μ,˜ν˜M−˜ρ˜μ,˜ν˜N+˜ρ˜μ,˜ν˜M˜ρ˜μ,˜ν˜N2−˜ρ˜μ,˜ν˜M−˜ρ˜μ,˜ν˜N−I∘(1−˜ρ˜μ,˜ν˜M)(1−˜ρ˜μ,˜ν˜N)=67, | (6.6) |
and to sum up,
1718≤˜ρ˜μ,˜ν˜M∩˜N(A)≤203,3≤˜ρ˜μ,˜ν˜M∩˜N(B)≤67. |
Obviously, the roughness of B classification is smaller.
If the traditional disturbation fuzzy set roughness measure calculation method is
˜ρμ,ν˜M∩˜N=1−|(S_(˜M∩˜N))μ||(ˉS(˜M∩˜N))ν|=1−|(S_(˜M))μ∩(S_(˜N))μ||(ˉS(˜M∩˜N))ν|, | (7.1) |
we need to calculate the number of equivalence classes after the intersection of (S_(˜M))μ and (S_(˜N))μ.
In Tables 3 and 5, the approximate values of the mathematical and verbal intersection of the disturbed fuzzy set caused by A classification and B classification are listed, respectively. It can be seen that the traditional method is more complicated to calculate. However, it can be seen from the example that using the method proposed in this paper to avoid complex calculation can effectively improve the work efficiency. This paper only lists 2 classification methods for 6 students. In practical problems, there may be tens of thousands of students' classification methods, etc. Therefore, when the sample size is large, the roughness measurement boundary of the disturbation fuzzy set proposed in this paper will greatly reduce the workload in operation. In practical problems with large datasets, such as when we need to do data mining, bioinformatics, cybersecurity, natural language processing, etc., the sample size is often huge. Therefore, it is usually better to determine the range of roughness first and then calculate in a small range.
First, this work effectively solves the problem that the execution subsets are not equal sets, which hindrances the quantitative study of disturbed fuzzy sets.
Second, through quantitative research, the new properties of the disturbation fuzzy set operation and the boundary of the roughness of the disturbation fuzzy set are established effectively, which can effectively reduce the workload in the operation when the actual data capacity is huge.
This paper proposes and proves that the roughness measure of the disturbed fuzzy set is bounded. In practical application, a full understanding of the roughness measure boundary of the disturbed fuzzy set can effectively avoid unnecessary computing space and greatly improve work efficiency. However, the roughness measurement of disturbed fuzzy sets depends on the choice of parameter μ,ν. The roughness measurement of disturbed fuzzy sets without parameters will be further explored in future work.
The authors declare they have not used Artificial Intelligence (AI) tools in the creation of this article.
This work was supported by the National Natural Science Foundation of China (No. 61603055).
Li Li: responsible for the planning, design and implementation of the research, providing financial and technical support. Hangyu Shi: designed research methods, processed and analyzed data, performed theorem proving, and wrote the first draft of the paper. Xiaona Liu: assisted in paper analysis and verification, and participated in paper revision. Jingjun Shi: provide partial data and coordinate the study as a whole.
The authors declare no conflicts of interest.
[1] |
Huai P, Li F, Chu T, et al. (2020) Prevalence of genital Chlamydia trachomatis infection in the general population: a meta-analysis. BMC Infect Dis 20: 1-8. https://doi.org/10.1186/s12879-020-05307-w ![]() |
[2] |
Herweg JA, Rudel T (2016) Interaction of Chlamydiae with human macrophages. The FEBS J 283: 608-618. https://doi.org/10.1111/febs.13609 ![]() |
[3] |
Scherler A, Jacquier N, Kebbi-Beghdadi C, et al. (2020) Diverse stress-inducing treatments cause distinct aberrant body morphologies in the Chlamydia-related bacterium, Waddlia chondrophila. Microorganisms 8: 89. https://doi.org/10.3390/microorganisms8010089 ![]() |
[4] |
Miyairi I, Mahdi OS, Ouellette SP, et al. (2006) Different growth rates of Chlamydia trachomatis biovars reflect pathotype. J Infect Dis 194: 350-357. https://doi.org/10.1086/505432 ![]() |
[5] |
Wilson D, Mathews S, Wan C, et al. (2004) Use of a quantitative gene expression assay based on micro-array techniques and a mathematical model for the investigation of chlamydial generation time. Bull Math Biology 66: 523-537. https://doi.org/10.1016/j.bulm.2003.09.001 ![]() |
[6] | Malhotra M, Sood S, Mukherjee A, et al. (2013) Genital Chlamydia trachomatis: an update. Indian J Med Res 138: 303-316. |
[7] | Zielecki J Establishment of in vitro-infection models for Chlamydia trachomatis based on human primary cells and primary tissue (2011). |
[8] |
Abu-Lubad M, Meyer TF, Al-Zeer MA (2014) Chlamydia trachomatis inhibits inducible NO synthase in human mesenchymal stem cells by stimulating polyamine synthesis. J Immunol 193: 2941-2951. https://doi.org/10.4049/jimmunol.1400377 ![]() |
[9] | Orciani M, Caffarini M, Lazzarini R, et al. (2018) Mesenchymal stem cells from cervix and age: new insights into CIN regression rate. Oxi Med Cell Longevity 2018: 1545784. https://doi.org/10.1155/2018/1545784 |
[10] |
Yan Z, Guo F, Yuan Q, et al. (2019) Endometrial mesenchymal stem cells isolated from menstrual blood repaired epirubicin-induced damage to human ovarian granulosa cells by inhibiting the expression of Gadd45b in cell cycle pathway. Stem Cell Res Ther 10: 1-10. https://doi.org/10.1186/s13287-018-1101-0 ![]() |
[11] |
Bishop RC, Boretto M, Rutkowski MR, et al. (2020) Murine endometrial organoids to model Chlamydia infection. Front Cell Infect Microbiol 10: 416. https://doi.org/10.3389/fcimb.2020.00416 ![]() |
[12] |
Chan RW, Schwab KE, Gargett CE (2004) Clonogenicity of human endometrial epithelial and stromal cells. Biolo Reprod 70: 1738-1750. https://doi.org/10.1095/biolreprod.103.024109 ![]() |
[13] |
Lu J, Zhu L, Zhang L, et al. (2017) Abnormal expression of TRAIL receptors in decidual tissue of Chlamydia trachomatis-infected rats during early pregnancy loss. Reprod Sci 24: 1041-1052. https://doi.org/10.1177/1933719116676393 ![]() |
[14] |
Gargett CE (2007) Uterine stem cells: what is the evidence?. Hum Reprod Update 13: 87-101. https://doi.org/10.1093/humupd/dml045 ![]() |
[15] |
Jazedje T, Perin PM, Czeresnia CE, et al. (2009) Human fallopian tube: a new source of multipotent adult mesenchymal stem cells discarded in surgical procedures. J Transl Med 7: 1-10. https://doi.org/10.1186/1479-5876-7-46 ![]() |
[16] |
Xia M, Bumgarner RE, Lampe MF, et al. (2003) Chlamydia trachomatis infection alters host cell transcription in diverse cellular pathways. J Infect Dis 187: 424-434. https://doi.org/10.1086/367962 ![]() |
[17] |
Al-Zeer MA, Al-Younes HM, Lauster D, et al. (2013) Autophagy restricts Chlamydia trachomatis growth in human macrophages via IFNG-inducible guanylate binding proteins. Autophagy 9: 50-62. https://doi.org/10.4161/auto.22482 ![]() |
[18] |
Al-Zeer MA, Xavier A, Lubad MA, et al. (2017) Chlamydia trachomatis prevents apoptosis via activation of PDPK1-MYC and enhanced mitochondrial binding of hexokinase II. EBioMedicine 23: 100-110. https://doi.org/10.1016/j.ebiom.2017.08.005 ![]() |
[19] |
Balsara ZR, Misaghi S, Lafave JN, et al. (2006) Chlamydia trachomatis infection induces cleavage of the mitotic cyclin B1. Infect Immun 74: 5602-5608. https://doi.org/10.1128/IAI.00266-06 ![]() |
[20] |
Fischer SF, Vier J, Kirschnek S, et al. (2004) Chlamydia inhibit host cell apoptosis by degradation of proapoptotic BH3-only proteins. J Exp Med 200: 905-916. https://doi.org/10.1084/jem.20040402 ![]() |
[21] | González E, Rother M, Kerr MC, et al. (2014) Chlamydia infection depends on a functional MDM2-p53 axis. Nat Commun 5: 1-10. https://doi.org/10.1038/ncomms6201 |
[22] |
García-Gutiérrez L, Bretones G, Molina E, et al. (2019) Myc stimulates cell cycle progression through the activation of Cdk1 and phosphorylation of p27. Sci Rep 9: 1-17. https://doi.org/10.1038/s41598-019-54917-1 ![]() |
[23] |
Kawauchi T (2014) C dk5 regulates multiple cellular events in neural development, function and disease. Dev Growth Differ 56: 335-348. https://doi.org/10.1111/dgd.12138 ![]() |
[24] |
Niu Y, Xu J, Sun T (2019) Cyclin-dependent kinases 4/6 inhibitors in breast cancer: current status, resistance, and combination strategies. J Cancer 10: 5504. https://doi.org/10.7150/jca.32628 ![]() |
[25] |
Asghar U, Witkiewicz AK, Turner NC, et al. (2015) The history and future of targeting cyclin-dependent kinases in cancer therapy. Nat Rev Drug Discovery 14: 130-146. https://doi.org/10.1038/nrd4504 ![]() |
[26] |
Larrea MD, Wander SA, Slingerland J (2009) p27 as Jekyll and Hyde: regulation of cell cycle and cell motility. Cell Cycle 8: 3455-3461. https://doi.org/10.4161/cc.8.21.9789 ![]() |
[27] |
Alkarain A, Slingerland J (2003) Deregulation of p27 by oncogenic signaling and its prognostic significance in breast cancer. Breast Cancer Res 6: 1-9. https://doi.org/10.1186/bcr722 ![]() |
[28] |
Zhao D, Besser AH, Wander SA, et al. (2015) Cytoplasmic p27 promotes epithelial–mesenchymal transition and tumor metastasis via STAT3-mediated Twist1 upregulation. Oncogene 34: 5447-5459. https://doi.org/10.1038/onc.2014.473 ![]() |
[29] |
Eguchi H, Carpentier S, Kim S, et al. (2004) P27kip1 regulates the apoptotic response of gastric epithelial cells to Helicobacter pylori. Gut 53: 797-804. https://doi.org/10.1136/gut.2003.032144 ![]() |
[30] |
Kim SS, Meitner P, Konkin TA, et al. (2006) Altered expression of Skp2, c-Myc and p27 proteins but not mRNA after H. pylori eradication in chronic gastritis. Mod Pathol 19: 49-58. https://doi.org/10.1038/modpathol.3800476 ![]() |
[31] |
Yarmishyn A, Child ES, Elphick LM, et al. (2008) Differential regulation of the cyclin-dependent kinase inhibitors p21Cip1 and p27Kip1 by phosphorylation directed by the cyclin encoded by Murine Herpesvirus 68. Exp Cell Res 314: 204-212. https://doi.org/10.1016/j.yexcr.2007.09.016 ![]() |
[32] |
Munder M (2009) Arginase: an emerging key player in the mammalian immune system. Br J Pharmacol 158: 638-651. https://doi.org/10.1111/j.1476-5381.2009.00291.x ![]() |
[33] |
Choi SH, Kim SW, Choi DH, et al. (2000) Polyamine-depletion induces p27Kip1 and enhances dexamethasone-induced G1 arrest and apoptosis in human T lymphoblastic leukemia cells. Leuk Res 24: 119-127. https://doi.org/10.1016/S0145-2126(99)00161-7 ![]() |
[34] |
Tabib A, Bachrach U (1998) Polyamines induce malignant transformation in cultured NIH 3T3 fibroblasts. Int J Biochem Cell Biol 30: 135-146. https://doi.org/10.1016/S1357-2725(97)00073-3 ![]() |
[35] | Ravanko K, Järvinen K, Paasinen-Sohns A, et al. (2000) Loss of p27Kip1 from cyclin E/cyclin-dependent kinase (CDK) 2 but not from cyclin D1/CDK4 complexes in cells transformed by polyamine biosynthetic enzymes. Cancer Res 60: 5244-5253. |
[36] |
Koomoa D-LT, Geerts D, Lange I, et al. (2013) DFMO/eflornithine inhibits migration and invasion downstream of MYCN and involves p27Kip1 activity in neuroblastoma. Int J Oncol 42: 1219-1228. https://doi.org/10.3892/ijo.2013.1835 ![]() |
[37] |
Al-Younes HM, Rudel T, Brinkmann V, et al. (2001) Low iron availability modulates the course of Chlamydia pneumoniae infection. Cell Microbiol 3: 427-437. https://doi.org/10.1046/j.1462-5822.2001.00125.x ![]() |
[38] |
Hristova NR, Tagscherer KE, Fassl A, et al. (2013) Notch1-dependent regulation of p27 determines cell fate in colorectal cancer. Intl J Oncol 43: 1967-1975. https://doi.org/10.3892/ijo.2013.2140 ![]() |
[39] |
Zhu H, Shen Z, Luo H, et al. (2016) Chlamydia trachomatis infection-associated risk of cervical cancer: a meta-analysis. Medicine 95: e3077. https://doi.org/10.1097/MD.0000000000003077 ![]() |
[40] |
Stone KM, Zaidi A, Rosero-Bixby L, et al. (1995) Sexual behavior, sexually transmitted diseases, and risk of cervical cancer. Epidemiology : 409-414. https://doi.org/10.1097/00001648-199507000-00014 ![]() |
[41] |
Farivar TN, Johari P (2012) Lack of association between Chlamydia trachomatis infection and cervical cancer-Taq Man realtime PCR assay findings. Asian Pac J Cancer Prev 13: 3701-3704. https://doi.org/10.7314/APJCP.2012.13.8.3701 ![]() |
[42] |
Tungsrithong N, Kasinpila C, Maneenin C, et al. (2014) Lack of significant effects of Chlamydia trachomatis infection on cervical cancer risk in a nested case-control study in North-East Thailand. Asian Pac J Cancer Prev 15: 1497-1500. https://doi.org/10.7314/APJCP.2014.15.3.1497 ![]() |
[43] |
Zereu M, Zettler C, Cambruzzi E, et al. (2007) Herpes simplex virus type 2 and Chlamydia trachomatis in adenocarcinoma of the uterine cervix. Gynecol Oncol 105: 172-175. https://doi.org/10.1016/j.ygyno.2006.11.006 ![]() |
[44] |
Simonetti AC, de Lima Melo JH, de Souza PRE, et al. (2009) Immunological's host profile for HPV and Chlamydia trachomatis, a cervical cancer cofactor. Microbes Infect 11: 435-442. https://doi.org/10.1016/j.micinf.2009.01.004 ![]() |
[45] |
Gunin AG, Glyakin DS, Emelianov VU (2021) Mycoplasma and Chlamydia infection can increase risk of endometrial cancer by pro-inflammatory cytokine enlargement. Indian J Gynecol Oncol 19: 1-7. https://doi.org/10.1007/s40944-020-00477-6 ![]() |
[46] | Parazzini F, La Vecchia C, Negri E, et al. (1996) Pelvic inflammatory disease and risk of ovarian cancer. Cancer Epidemiol Biomarkers Prve 5: 667-669. |
[47] |
Richards TS, Knowlton AE, Grieshaber SS (2013) Chlamydia trachomatis homotypic inclusion fusion is promoted by host microtubule trafficking. BMC Microbiol 13: 1-8. https://doi.org/10.1186/1471-2180-13-185 ![]() |
[48] |
Koskela P, Anttila T, Bjørge T, et al. (2000) Chlamydia trachomatis infection as a risk factor for invasive cervical cancer. Int J Cancer 85: 35-39. https://doi.org/10.1002/(SICI)1097-0215(20000101)85:1<35::AID-IJC6>3.0.CO;2-A ![]() |
[49] |
Smith JS, Bosetti C, MUnoz N, et al. (2004) Chlamydia trachomatis and invasive cervical cancer: A pooled analysis of the IARC multicentric case-control study. Int J Cancer 111: 431-439. https://doi.org/10.1002/ijc.20257 ![]() |
[50] |
Smith JS, Muñoz N, Herrero R, et al. (2002) Evidence for Chlamydia trachomatis as a human papillomavirus cofactor in the etiology of invasive cervical cancer in Brazil and the Philippines. J Infect Dis 185: 324-331. https://doi.org/10.1086/338569 ![]() |
[51] |
Hinkula M, Pukkala E, Kyyrönen P, et al. (2004) A population-based study on the risk of cervical cancer and cervical intraepithelial neoplasia among grand multiparous women in Finland. Bri J Cancer 90: 1025-1029. https://doi.org/10.1038/sj.bjc.6601650 ![]() |
[52] |
Lindahl T, Barnes D (2000) Repair of endogenous DNA damage. Cold Spring Harb Symp Quant Biol 65: 127-134. https://doi.org/10.1101/sqb.2000.65.127 ![]() |
[53] |
Coombes BK, Mahony JB (1999) Chlamydia pneumoniae infection of human endothelial cells induces proliferation of smooth muscle cells via an endothelial cell-derived soluble factor (s). Infect Immun 67: 2909-2915. https://doi.org/10.1128/IAI.67.6.2909-2915.1999 ![]() |
[54] |
Chiou C-C, Chan C-C, Kuo Y-P, et al. (2003) Helicobacter pylori inhibits activity of cdc2 kinase and delays G 2/M to G 1 progression in gastric adenocarcinoma cell. Scand J Gastroenterol 38: 147-152. https://doi.org/10.1080/00365520310000627 ![]() |
[55] |
Nougayrède J-P, Boury M, Tasca C, et al. (2001) Type III secretion-dependent cell cycle block caused in HeLa cells by enteropathogenic Escherichia coli O103. Infect Immun 69: 6785-6795. https://doi.org/10.1128/IAI.69.11.6785-6795.2001 ![]() |
[56] |
Davy CE, Jackson DJ, Raj K, et al. (2005) Human papillomavirus type 16 E1∧ E4-induced G2 arrest is associated with cytoplasmic retention of active Cdk1/cyclin B1 complexes. J Virol 79: 3998-4011. https://doi.org/10.1128/JVI.79.7.3998-4011.2005 ![]() |
[57] |
Poggioli GJ, Dermody TS, Tyler KL (2001) Reovirus-induced ς1s-dependent G2/M phase cell cycle arrest is associated with inhibition of p34cdc2. J Virol 75: 7429-7434. https://doi.org/10.1128/JVI.75.16.7429-7434.2001 ![]() |
[58] |
He J, Choe S, Walker R, et al. (1995) Human immunodeficiency virus type 1 viral protein R (Vpr) arrests cells in the G2 phase of the cell cycle by inhibiting p34cdc2 activity. J Virol 69: 6705-6711. https://doi.org/10.1128/jvi.69.11.6705-6711.1995 ![]() |
[59] |
Slingerland J, Pagano M (2000) Regulation of the cdk inhibitor p27 and its deregulation in cancer. J Cell Physiol 183: 10-17. https://doi.org/10.1002/(SICI)1097-4652(200004)183:1<10::AID-JCP2>3.0.CO;2-I ![]() |
[60] |
Porter PL, Malone KE, Heagerty PJ, et al. (1997) Expression of cell-cycle regulators p27Kip1 and cyclin E, alone and in combination, correlate with survival in young breast cancer patients. Nat Med 3: 222-225. https://doi.org/10.1038/nm0297-222 ![]() |
[61] |
Catzavelos C, Bhattacharya N, Ung YC, et al. (1997) Decreased levels of the cell-cycle inhibitor p27Kip1 protein: prognostic implications in primary breast cancer. Nat Med 3: 227-230. https://doi.org/10.1038/nm0297-227 ![]() |
[62] |
Nakayama K, Ishida N, Shirane M, et al. (1996) Mice lacking p27Kip1 display increased body size, multiple organ hyperplasia, retinal dysplasia, and pituitary tumors. Cell 85: 707-720. https://doi.org/10.1016/S0092-8674(00)81237-4 ![]() |
[63] |
Fujita N, Sato S, Katayama K, et al. (2002) Akt-dependent phosphorylation of p27Kip1 promotes binding to 14-3-3 and cytoplasmic localization. J Biol Chem 277: 28706-28713. https://doi.org/10.1074/jbc.M203668200 ![]() |
[64] |
Tsvetkov LM, Yeh K-H, Lee S-J, et al. (1999) p27Kip1 ubiquitination and degradation is regulated by the SCFSkp2 complex through phosphorylated Thr187 in p27. Curr Biol 9: 661-S662. https://doi.org/10.1016/S0960-9822(99)80290-5 ![]() |
[65] |
Hengst L, Reed SI (1996) Translational control of p27Kip1 accumulation during the cell cycle. Science 271: 1861-1864. https://doi.org/10.1126/science.271.5257.1861 ![]() |
[66] | Eguchi H, Herschenhous N, Kuzushita N, et al. (2003) Helicobacter pylori increases proteasome-mediated degradation of p27kip1 in gastric epithelial cells. Cancer Res 63: 4739-4746. |
[67] |
Wen S, So Y, Singh K, et al. (2012) Promotion of cytoplasmic mislocalization of p27 by Helicobacter pylori in gastric cancer. Oncogene 31: 1771-1780. https://doi.org/10.1038/onc.2011.362 ![]() |
[68] |
Sekimoto T, Fukumoto M, Yoneda Y (2004) 14-3-3 suppresses the nuclear localization of threonine 157-phosphorylated p27Kip1. EMBO J 23: 1934-1942. https://doi.org/10.1038/sj.emboj.7600198 ![]() |
[69] |
Ishida N, Hara T, Kamura T, et al. (2002) Phosphorylation of p27Kip1 on serine 10 is required for its binding to CRM1 and nuclear export. J Biol Chem 277: 14355-14358. https://doi.org/10.1074/jbc.C100762200 ![]() |
[70] |
Kotoshiba S, Gopinathan L, Pfeiffenberger E, et al. (2014) p27 is regulated independently of Skp2 in the absence of Cdk2. Biochim Biophy Acta Mol Cell Res 1843: 436-445. https://doi.org/10.1016/j.bbamcr.2013.11.005 ![]() |
[71] |
Short JD, Dere R, Houston KD, et al. (2010) AMPK-mediated phosphorylation of murine p27 at T197 promotes binding of 14-3-3 proteins and increases p27 stability. Mol Carcinog 49: 429-439. https://doi.org/10.1002/mc.20613 ![]() |
[72] |
Koomoa D-LT, Yco LP, Borsics T, et al. (2008) Ornithine decarboxylase inhibition by α-difluoromethylornithine activates opposing signaling pathways via phosphorylation of both Akt/protein kinase B and p27Kip1 in neuroblastoma. Cancer Res 68: 9825-9831. https://doi.org/10.1158/0008-5472.CAN-08-1865 ![]() |
[73] |
Martín A, Odajima J, Hunt SL, et al. (2005) Cdk2 is dispensable for cell cycle inhibition and tumor suppression mediated by p27Kip1 and p21Cip1. Cancer Cell 7: 591-598. https://doi.org/10.1016/j.ccr.2005.05.006 ![]() |
[74] | Krysenko S, Wohlleben W (2022) Polyamine and ethanolamine metabolism in bacteria as an important component of nitrogen assimilation for survival and pathogenicity. Med Sci 10: 40. https://doi.org/10.3390/medsci10030040 |
[75] |
Knowlton AE, Fowler LJ, Patel RK, et al. (2013) Chlamydia induces anchorage independence in 3T3 cells and detrimental cytological defects in an infection model. PLOS One 8: e54022. https://doi.org/10.1371/journal.pone.0054022 ![]() |
[76] |
Kumar A, Tripathy MK, Pasquereau S, et al. (2018) The human cytomegalovirus strain DB activates oncogenic pathways in mammary epithelial cells. EBioMedicine 30: 167-183. https://doi.org/10.1016/j.ebiom.2018.03.015 ![]() |
[77] |
Chen AL, Johnson KA, Lee JK, et al. (2012) CPAF: a Chlamydial protease in search of an authentic substrate. PLoS Pathog 8: e1002842. https://doi.org/10.1371/journal.ppat.1002842 ![]() |
1. | Li Li, Jin Yang, Disturbing Fuzzy Multi-Attribute Decision-Making Method with If Weight Information Is Disturbing Fuzzy Number, 2024, 12, 2227-7390, 1225, 10.3390/math12081225 |
Student 1 | Student 2 | Student 3 | Student 4 | Student 5 | Student 6 | |
˜M | (0.80,0.09) | (0.30,0.01) | (0.66,0.06) | (0.61,0.23) | (0.43,0.05) | (0.60,0.10) |
˜N | (0.80,0.09) | (0.75,0.21) | (0.45,0.08) | (0.70,0.09) | (0.64,0.03) | (0.50,0.14) |
Student 1 | Student 2,Student 3,Student 5 | Student 4,Student 6 | |
S_(˜M) | (0.80,0.09) | (0.30,0.06) | (0.60,0.23) |
S_(˜N) | (0.66,0.03) | (0.45,0.21) | (0.50,0.14) |
ˉS(˜N) | (0.66,0.03) | (0.75,0.03) | (0.70,0.09) |
Student 1 | Student 2,Student 3,Student 5 | Student 4,Student 6 | |
S_(˜M∪˜N) | (0.80,0.03) | (0.64,0.06) | (0.60,0.09) |
ˉS(˜M∪˜N) | (0.66,0.09) | (0.75,0.01) | (0.70,0.01) |
S_(˜M∩˜N) | (0.66,0.09) | (0.30,0.21) | (0.50,0.23) |
ˉS(˜M∩˜N) | (0.66,0.09) | (0.45,0.05) | (0.61,0.14) |
Student 1,Student 4 | Student 2,Student 5 | Student 3,Student 6 | |
S_(˜M) | (0.61,0.23) | (0.30,0.05) | (0.60,0.10) |
ˉS(˜M) | (0.80,0.09) | (0.43,0.01) | (0.66,0.06) |
S_(˜N) | (0.66,0.09) | (0.64,0.21) | (0.45,0.14) |
ˉS(˜N) | (0.70,0.03) | (0.75,0.03) | (0.50,0.08) |
Student 1,Student 4 | Student 2,Student 5 | Student 3,Student 6 | |
S_(˜M∪˜N) | (0.70,0.09) | (0.64,0.03) | (0.60,0.10) |
ˉS(˜M∪˜N) | (0.80,0.03) | (0.75,0.01) | (0.66,0.06) |
S_(˜M∩˜N) | (0.61,0.23) | (0.30,0.21) | (0.45,0.14) |
ˉS(˜M∩˜N) | (0.66,0.09) | (0.43,0.05) | (0.50,0.08) |
Student 1 | Student 2 | Student 3 | Student 4 | Student 5 | Student 6 | |
˜M | (0.80,0.09) | (0.30,0.01) | (0.66,0.06) | (0.61,0.23) | (0.43,0.05) | (0.60,0.10) |
˜N | (0.80,0.09) | (0.75,0.21) | (0.45,0.08) | (0.70,0.09) | (0.64,0.03) | (0.50,0.14) |
Student 1 | Student 2,Student 3,Student 5 | Student 4,Student 6 | |
S_(˜M) | (0.80,0.09) | (0.30,0.06) | (0.60,0.23) |
S_(˜N) | (0.66,0.03) | (0.45,0.21) | (0.50,0.14) |
ˉS(˜N) | (0.66,0.03) | (0.75,0.03) | (0.70,0.09) |
Student 1 | Student 2,Student 3,Student 5 | Student 4,Student 6 | |
S_(˜M∪˜N) | (0.80,0.03) | (0.64,0.06) | (0.60,0.09) |
ˉS(˜M∪˜N) | (0.66,0.09) | (0.75,0.01) | (0.70,0.01) |
S_(˜M∩˜N) | (0.66,0.09) | (0.30,0.21) | (0.50,0.23) |
ˉS(˜M∩˜N) | (0.66,0.09) | (0.45,0.05) | (0.61,0.14) |
Student 1,Student 4 | Student 2,Student 5 | Student 3,Student 6 | |
S_(˜M) | (0.61,0.23) | (0.30,0.05) | (0.60,0.10) |
ˉS(˜M) | (0.80,0.09) | (0.43,0.01) | (0.66,0.06) |
S_(˜N) | (0.66,0.09) | (0.64,0.21) | (0.45,0.14) |
ˉS(˜N) | (0.70,0.03) | (0.75,0.03) | (0.50,0.08) |
Student 1,Student 4 | Student 2,Student 5 | Student 3,Student 6 | |
S_(˜M∪˜N) | (0.70,0.09) | (0.64,0.03) | (0.60,0.10) |
ˉS(˜M∪˜N) | (0.80,0.03) | (0.75,0.01) | (0.66,0.06) |
S_(˜M∩˜N) | (0.61,0.23) | (0.30,0.21) | (0.45,0.14) |
ˉS(˜M∩˜N) | (0.66,0.09) | (0.43,0.05) | (0.50,0.08) |