Pub Date : 2024-11-29DOI: 10.1016/j.fss.2024.109218
Yi Shi
Fuzzy betweenness relations have gained increasing attention since Zhang et al. recently established their extensive connections with fuzzy order relations. In this manuscript, we delve into the exploration of strict fuzzy betweenness relations from two aspects. First of all, in light of one of the most important examples of strict betweenness relations from strict order relations, we extend this paradigm to the fuzzy case. Specially, with respect to a t-norm ⁎ and a fuzzy equivalence relation E, we construct a strict ⁎-E-betweenness relation from a strict ⁎-E-order relation. Secondly, by establishing a one-to-one correspondence between strict betweenness relations and betweenness relations, we investigate whether this elegant result persists within the many-valued setting. Toward this end, we present the construction of a strict fuzzy betweenness relation from a fuzzy betweenness relation and vice versa, scrutinizing the conditions under which these constructions are inverse to each other. The conclusion turns out that the correspondence in the fuzzy context exhibits distinct differences from the crisp one, primarily due to the inherent complexity of fuzzy logic.
{"title":"On strict fuzzy betweenness relations","authors":"Yi Shi","doi":"10.1016/j.fss.2024.109218","DOIUrl":"10.1016/j.fss.2024.109218","url":null,"abstract":"<div><div>Fuzzy betweenness relations have gained increasing attention since Zhang et al. recently established their extensive connections with fuzzy order relations. In this manuscript, we delve into the exploration of strict fuzzy betweenness relations from two aspects. First of all, in light of one of the most important examples of strict betweenness relations from strict order relations, we extend this paradigm to the fuzzy case. Specially, with respect to a t-norm ⁎ and a fuzzy equivalence relation <em>E</em>, we construct a strict ⁎-<em>E</em>-betweenness relation from a strict ⁎-<em>E</em>-order relation. Secondly, by establishing a one-to-one correspondence between strict betweenness relations and betweenness relations, we investigate whether this elegant result persists within the many-valued setting. Toward this end, we present the construction of a strict fuzzy betweenness relation from a fuzzy betweenness relation and vice versa, scrutinizing the conditions under which these constructions are inverse to each other. The conclusion turns out that the correspondence in the fuzzy context exhibits distinct differences from the crisp one, primarily due to the inherent complexity of fuzzy logic.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"501 ","pages":"Article 109218"},"PeriodicalIF":3.2,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142743982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-23DOI: 10.1016/j.fss.2024.109204
Zhen Wang , Yanbo Chen , Yanyan Ni , Xia Huang , Hao Shen
This paper is concerned with data-driven event-triggered control for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems subject to actuator saturation. Based on the proposed event-triggered mechanism (ETM) and the discrete-time Lyapunov stability theory, a model-based stability criterion for the known T-S fuzzy system is derived first. Subsequently, by leveraging the input-state data collected from each local subsystem, a data-based system representation of unknown T-S fuzzy system is established and a pure data-based stability criterion in the form of linear matrix inequalities (LMIs) is obtained to guarantee that the T-S fuzzy system with unknown system matrices is locally stabilized. Meanwhile, a joint design algorithm for the data-driven fuzzy controllers and the ETM is accomplished. Compared with the other data-driven control methods, the proposed method has the advantages of simplicity and flexibility for some control problems whose stability results satisfy a certain LMI form. At last, the effectiveness of the model-based and data-based results is verified through a numerical example, and the influence of some key factors, such as the number of samples and the noise on control performance is investigated by estimating the inner-approximation of the basin of attraction (BoA) and the outer-approximation of the attractor.
{"title":"Data-driven event-triggered control for discrete-time T-S fuzzy systems subject to actuator saturation","authors":"Zhen Wang , Yanbo Chen , Yanyan Ni , Xia Huang , Hao Shen","doi":"10.1016/j.fss.2024.109204","DOIUrl":"10.1016/j.fss.2024.109204","url":null,"abstract":"<div><div>This paper is concerned with data-driven event-triggered control for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems subject to actuator saturation. Based on the proposed event-triggered mechanism (ETM) and the discrete-time Lyapunov stability theory, a model-based stability criterion for the known T-S fuzzy system is derived first. Subsequently, by leveraging the input-state data collected from each local subsystem, a data-based system representation of unknown T-S fuzzy system is established and a pure data-based stability criterion in the form of linear matrix inequalities (LMIs) is obtained to guarantee that the T-S fuzzy system with unknown system matrices is locally stabilized. Meanwhile, a joint design algorithm for the data-driven fuzzy controllers and the ETM is accomplished. Compared with the other data-driven control methods, the proposed method has the advantages of simplicity and flexibility for some control problems whose stability results satisfy a certain LMI form. At last, the effectiveness of the model-based and data-based results is verified through a numerical example, and the influence of some key factors, such as the number of samples and the noise on control performance is investigated by estimating the inner-approximation of the basin of attraction (BoA) and the outer-approximation of the attractor.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"501 ","pages":"Article 109204"},"PeriodicalIF":3.2,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142720779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-22DOI: 10.1016/j.fss.2024.109216
Antonio Francisco Roldán López de Hierro , Concepción Roldán , Carlos Guerra , Javier Fernández , Anderson Cruz , Ronei Marcos de Moraes , Humberto Bustince
In this work, we introduce the notion of grouping index for type-2 fuzzy sets as a measure of how far the union of two type-2 fuzzy sets over the same universe is from the total universe. We also show how we can extend the notion of the Jaccard index to the type-2 setting by means of type-2 grouping and overlap indexes.
{"title":"From type-(2,k) grouping indices to type-(2,k) Jaccard indices","authors":"Antonio Francisco Roldán López de Hierro , Concepción Roldán , Carlos Guerra , Javier Fernández , Anderson Cruz , Ronei Marcos de Moraes , Humberto Bustince","doi":"10.1016/j.fss.2024.109216","DOIUrl":"10.1016/j.fss.2024.109216","url":null,"abstract":"<div><div>In this work, we introduce the notion of grouping index for type-2 fuzzy sets as a measure of how far the union of two type-2 fuzzy sets over the same universe is from the total universe. We also show how we can extend the notion of the Jaccard index to the type-2 setting by means of type-2 grouping and overlap indexes.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"501 ","pages":"Article 109216"},"PeriodicalIF":3.2,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142699699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-20DOI: 10.1016/j.fss.2024.109202
Yue Hu , Oh-Min Kwon , Seung-Hoon Lee
The control of the interval type-2 (IT2) fuzzy singularly perturbed systems (SPSs) with packet losses is studied in this paper. To alleviate data collision, a multi-node round-robin protocol (RRP) is adopted to decide the communication sequences between the sensors and controller. With the help of multi-node RRP, only partial sensor nodes have the priority to access the network channels at each instant. Meanwhile, a Bernoulli packet dropout model is used to further analyze the occurrence of packet dropouts during data transmission. This article's main research results and contributions consist of two parts: (1) Firstly, by combining multi-node RRP, Bernoulli packet loss model and mismatched membership functions, an IT2 fuzzy controller dependent on scheduling state information is designed, under which the control performance of the system can be effectively enhanced. (2) Secondly, by establishing a new Lyapunov functional related to singular perturbation parameter, the system stability conditions can be obtained and ill-conditioned issue is alleviated. Eventually, the feasibility of developed method is validated by the Van der Pol circuit system example.
本文研究了具有数据包丢失的区间型-2（IT2）模糊奇异扰动系统（SPS）的 H∞ 控制。为了减少数据碰撞，本文采用了多节点循环协议（RRP）来决定传感器和控制器之间的通信顺序。在多节点轮循协议的帮助下，每一瞬间只有部分传感器节点有访问网络信道的优先权。同时，采用伯努利丢包模型进一步分析数据传输过程中丢包现象的发生。本文的主要研究成果和贡献包括两部分：（1）首先，结合多节点 RRP、伯努利丢包模型和错配成员函数，设计了一种依赖于调度状态信息的 IT2 模糊控制器，在此控制器下，系统的控制性能可以得到有效提升。(2) 其次，通过建立与奇异扰动参数相关的新 Lyapunov 函数，可以获得系统稳定性条件，并缓解了无条件问题。最后，以 Van der Pol 电路系统为例，验证了所开发方法的可行性。
{"title":"H∞ control for interval type-2 fuzzy singularly perturbed systems with multi-node round-robin protocol and packet dropouts","authors":"Yue Hu , Oh-Min Kwon , Seung-Hoon Lee","doi":"10.1016/j.fss.2024.109202","DOIUrl":"10.1016/j.fss.2024.109202","url":null,"abstract":"<div><div>The <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> control of the interval type-2 (IT2) fuzzy singularly perturbed systems (SPSs) with packet losses is studied in this paper. To alleviate data collision, a multi-node round-robin protocol (RRP) is adopted to decide the communication sequences between the sensors and controller. With the help of multi-node RRP, only partial sensor nodes have the priority to access the network channels at each instant. Meanwhile, a Bernoulli packet dropout model is used to further analyze the occurrence of packet dropouts during data transmission. This article's main research results and contributions consist of two parts: (1) Firstly, by combining multi-node RRP, Bernoulli packet loss model and mismatched membership functions, an IT2 fuzzy controller dependent on scheduling state information is designed, under which the control performance of the system can be effectively enhanced. (2) Secondly, by establishing a new Lyapunov functional related to singular perturbation parameter, the system stability conditions can be obtained and ill-conditioned issue is alleviated. Eventually, the feasibility of developed method is validated by the Van der Pol circuit system example.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"500 ","pages":"Article 109202"},"PeriodicalIF":3.2,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142703346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-19DOI: 10.1016/j.fss.2024.109205
Daniel Leite , Gabriella Casalino , Katarzyna Kaczmarek-Majer , Giovanna Castellano
We apply an evolving granular-computing modeling approach, called evolving Optimal Granular System (eOGS), to bipolar mood disorder (BD) diagnosis based on speech data streams. The eOGS online learning algorithm reveals information granules in the flow and design the structure and parameters of a granular rule-based model with a certain degree of interpretability based on acoustic attributes obtained from phone calls made over 7 months to the Psychiatry department of a hospital. A multi-objective programming problem that trades-off information specificity, model compactness, and numerical and granular error indices is presented. Spectral and prosodic attributes are ranked and selected based on a hybrid Pearson-Spearman correlation coefficient. Low attribute-class correlation, ranging from 0.03 to 0.07, is observed, as well as high class overlap, which is typical in the psychiatric field. eOGS models for BD recognition overcome alternative computational-intelligence models, namely, Dynamic Evolving Neural-Fuzzy Inference System (DENFIS) and Fuzzy-set-Based evolving Modeling (FBeM-Gauss), by a small margin in both best and average cases; followed by eXtended Takagi-Sugeno (xTS) and evolving Takagi Sugeno (eTS) types of models. The proposed eOGS model using only 8 of the original acoustic attributes, and about 15 ‘If-Then’ inference rules, has exhibited the best root mean square error, 0.1361, and 91.8% accuracy in sharp BD class estimates. Granules associated to linguistic labels and a granular input-output map offer human understandability with relation to the inherent process of generating class estimates. Linguistically readable eOGS rules may assist physicians in explaining symptoms and making a diagnosis.
{"title":"Incremental learning and granular computing from evolving data streams: An application to speech-based bipolar disorder diagnosis","authors":"Daniel Leite , Gabriella Casalino , Katarzyna Kaczmarek-Majer , Giovanna Castellano","doi":"10.1016/j.fss.2024.109205","DOIUrl":"10.1016/j.fss.2024.109205","url":null,"abstract":"<div><div>We apply an evolving granular-computing modeling approach, called evolving Optimal Granular System (eOGS), to bipolar mood disorder (BD) diagnosis based on speech data streams. The eOGS online learning algorithm reveals information granules in the flow and design the structure and parameters of a granular rule-based model with a certain degree of interpretability based on acoustic attributes obtained from phone calls made over 7 months to the Psychiatry department of a hospital. A multi-objective programming problem that trades-off information specificity, model compactness, and numerical and granular error indices is presented. Spectral and prosodic attributes are ranked and selected based on a hybrid Pearson-Spearman correlation coefficient. Low attribute-class correlation, ranging from 0.03 to 0.07, is observed, as well as high class overlap, which is typical in the psychiatric field. eOGS models for BD recognition overcome alternative computational-intelligence models, namely, Dynamic Evolving Neural-Fuzzy Inference System (DENFIS) and Fuzzy-set-Based evolving Modeling (FBeM-Gauss), by a small margin in both best and average cases; followed by eXtended Takagi-Sugeno (xTS) and evolving Takagi Sugeno (eTS) types of models. The proposed eOGS model using only 8 of the original acoustic attributes, and about 15 ‘If-Then’ inference rules, has exhibited the best root mean square error, 0.1361, and 91.8% accuracy in sharp BD class estimates. Granules associated to linguistic labels and a granular input-output map offer human understandability with relation to the inherent process of generating class estimates. Linguistically readable eOGS rules may assist physicians in explaining symptoms and making a diagnosis.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"500 ","pages":"Article 109205"},"PeriodicalIF":3.2,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142703355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-19DOI: 10.1016/j.fss.2024.109199
Yao Ouyang , Yonghui Sun , Hua-Peng Zhang
The characterizations when two natural upper bounds of the set of copulas with a given diagonal section are copulas have been well studied in the literature. Given a curvilinear section, however, there is only a partial result concerning the characterization when a natural upper bound of the set of copulas is a copula. In this paper, we completely solve the characterization problem for this natural upper bound to be a copula in the curvilinear case.
{"title":"On an upper bound of the set of copulas with a given curvilinear section","authors":"Yao Ouyang , Yonghui Sun , Hua-Peng Zhang","doi":"10.1016/j.fss.2024.109199","DOIUrl":"10.1016/j.fss.2024.109199","url":null,"abstract":"<div><div>The characterizations when two natural upper bounds of the set of copulas with a given diagonal section are copulas have been well studied in the literature. Given a curvilinear section, however, there is only a partial result concerning the characterization when a natural upper bound of the set of copulas is a copula. In this paper, we completely solve the characterization problem for this natural upper bound to be a copula in the curvilinear case.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"500 ","pages":"Article 109199"},"PeriodicalIF":3.2,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142703356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-19DOI: 10.1016/j.fss.2024.109203
Lanshuang Zhang , Zhenhua Wang , Choon Ki Ahn , Yi Shen
This paper proposes a fault detection scheme via a zonotopic fuzzy filter for Takagi-Sugeno (T-S) fuzzy systems by considering unknown but bounded parametric uncertainties, disturbances, noises, and actuator faults, which is more consistent with practical systems. First, we design a fuzzy fault detection filter to obtain robust residuals. The optimal gain matrix of the designed filter is computed offline, which can reduce the computational burden and improve fault detection efficiency. Second, zonotopic analysis is used to obtain the guaranteed adaptive residual thresholds. Third, the residual generation and evaluation scheme through the zonotopic analysis are presented. To illustrate the superiority of the proposed scheme, a numerical simulation comparison is studied. Compared with the existing method, the proposed scheme has a more concise and simpler design process, which can offer adaptive guaranteed thresholds and detect the fault more accurately. Finally, a vehicle lateral system is used to justify the validity and applicability of the presented fault detection scheme.
{"title":"Fault detection for T-S nonlinear systems with parametric uncertainties via zonotopic H∞ filter","authors":"Lanshuang Zhang , Zhenhua Wang , Choon Ki Ahn , Yi Shen","doi":"10.1016/j.fss.2024.109203","DOIUrl":"10.1016/j.fss.2024.109203","url":null,"abstract":"<div><div>This paper proposes a fault detection scheme via a zonotopic fuzzy <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> filter for Takagi-Sugeno (T-S) fuzzy systems by considering unknown but bounded parametric uncertainties, disturbances, noises, and actuator faults, which is more consistent with practical systems. First, we design a fuzzy <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> fault detection filter to obtain robust residuals. The optimal gain matrix of the designed filter is computed offline, which can reduce the computational burden and improve fault detection efficiency. Second, zonotopic analysis is used to obtain the guaranteed adaptive residual thresholds. Third, the residual generation and evaluation scheme through the zonotopic analysis are presented. To illustrate the superiority of the proposed scheme, a numerical simulation comparison is studied. Compared with the existing <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>−</mo></mrow></msub><mo>/</mo><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> method, the proposed scheme has a more concise and simpler design process, which can offer adaptive guaranteed thresholds and detect the fault more accurately. Finally, a vehicle lateral system is used to justify the validity and applicability of the presented fault detection scheme.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"501 ","pages":"Article 109203"},"PeriodicalIF":3.2,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142699698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-19DOI: 10.1016/j.fss.2024.109179
G. Nguepy Dongmo , B.B. Koguep Njionou , L. Kwuida , M. Onabid
Multilattices are very suitable to deal with fuzziness in non-deterministic environments. In this paper, we propose an extension of the work of Shao et al. by replacing a residuated lattice with a multilattice, as the algebraic structure of truth values in the set approximations within fuzzy formal concept analysis. We propose new fuzzy concept multilattices derived from adjoint pairs. In addition, we define two pairs of rough fuzzy set approximations in fuzzy formal contexts via multilattice, and we establish their characterizations.
{"title":"Roughness in formal concept analysis via multilattices","authors":"G. Nguepy Dongmo , B.B. Koguep Njionou , L. Kwuida , M. Onabid","doi":"10.1016/j.fss.2024.109179","DOIUrl":"10.1016/j.fss.2024.109179","url":null,"abstract":"<div><div>Multilattices are very suitable to deal with fuzziness in non-deterministic environments. In this paper, we propose an extension of the work of Shao et al. by replacing a residuated lattice with a multilattice, as the algebraic structure of truth values in the set approximations within fuzzy formal concept analysis. We propose new fuzzy concept multilattices derived from adjoint pairs. In addition, we define two pairs of rough fuzzy set approximations in fuzzy formal contexts via multilattice, and we establish their characterizations.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"500 ","pages":"Article 109179"},"PeriodicalIF":3.2,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142703357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-19DOI: 10.1016/j.fss.2024.109201
Meng Chen, Yun-Mao Zhang, Xue-ping Wang
Consider a two-place function defined by where is an associative function, is a monotone function that satisfies either when or for any when for all and is a pseudo-inverse of f. In this article, the associativity of the function T is shown to depend only on properties of the range of f. The necessary and sufficient conditions for the T being associative are presented by applying the properties of the monotone function f.
考虑由 T(x,y)=f(-1)(F(f(x),f(y))定义的双位函数 T：[0,1]2→[0,1]，其中 F：[0,∞]2→[0,∞]是关联函数，f：[0,1]→[0,∞]是一个单调函数，当 f(x+)∈Ran(f) 时，满足 f(x)=f(x+) 或当 f(x+)∉Ran(f) 时，对于所有 x∈[0,1]，对于任意 y≠x，满足 f(x)≠f(y)；f(-1):[0,∞]→[0,1]是 f 的伪逆。本文证明了函数 T 的关联性只取决于 f 范围的性质，并应用单调函数 f 的性质提出了函数 T 关联性的必要条件和充分条件。
{"title":"The characterization of monotone functions that generate associative functions","authors":"Meng Chen, Yun-Mao Zhang, Xue-ping Wang","doi":"10.1016/j.fss.2024.109201","DOIUrl":"10.1016/j.fss.2024.109201","url":null,"abstract":"<div><div>Consider a two-place function <span><math><mi>T</mi><mo>:</mo><msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>→</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> defined by <span><math><mi>T</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>=</mo><msup><mrow><mi>f</mi></mrow><mrow><mo>(</mo><mo>−</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>(</mo><mi>F</mi><mo>(</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>f</mi><mo>(</mo><mi>y</mi><mo>)</mo><mo>)</mo><mo>)</mo></math></span> where <span><math><mi>F</mi><mo>:</mo><msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>]</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>→</mo><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>]</mo></math></span> is an associative function, <span><math><mi>f</mi><mo>:</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo><mo>→</mo><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>]</mo></math></span> is a monotone function that satisfies either <span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>f</mi><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo></math></span> when <span><math><mi>f</mi><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo><mo>∈</mo><mtext>Ran</mtext><mo>(</mo><mi>f</mi><mo>)</mo></math></span> or <span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>≠</mo><mi>f</mi><mo>(</mo><mi>y</mi><mo>)</mo></math></span> for any <span><math><mi>y</mi><mo>≠</mo><mi>x</mi></math></span> when <span><math><mi>f</mi><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo><mo>∉</mo><mtext>Ran</mtext><mo>(</mo><mi>f</mi><mo>)</mo></math></span> for all <span><math><mi>x</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> and <span><math><msup><mrow><mi>f</mi></mrow><mrow><mo>(</mo><mo>−</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>:</mo><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>]</mo><mo>→</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> is a pseudo-inverse of <em>f</em>. In this article, the associativity of the function <em>T</em> is shown to depend only on properties of the range of <em>f</em>. The necessary and sufficient conditions for the <em>T</em> being associative are presented by applying the properties of the monotone function <em>f</em>.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"500 ","pages":"Article 109201"},"PeriodicalIF":3.2,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142703353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-17DOI: 10.1016/j.fss.2024.109198
Yufeng Shen , Xueling Ma , Zeshui Xu , Muhammet Deveci , Jianming Zhan
The rise of social media and e-democracy has driven a paradigm shift in decision-making, notably reflected in the changing ways of public participation and policymaking within decision-making processes. The increased focus on fairness and efficiency not only complicates the consensus-building process among diverse interests and perspectives, but also significantly adds to the complexity of decision-making and its implementation. In this context, balancing the interests of all parties while ensuring fairness and improving decision-making effectiveness becomes crucial. To address these challenges, this study develops a multi-objective optimization consensus framework for large-scale group decision-making (LSGDM) that integrates the interests of decision-makers (DMs) and a moderator, providing a more comprehensive tool. Specifically, this study first designs a DM weight determination method based on structural hole theory within fuzzy social networks. The proposed DM weight determination method effectively leverages the flexibility of fuzzy social networks and the comprehensiveness of structural hole theory to enhance the accuracy and reliability of weight assignment. Building on this, a novel clustering method based on the maximum group consensus level is developed, taking into account the varying importance of different DMs. Furthermore, a minimum cost and maximum fairness-driven multi-objective optimization LSGDM consensus model, referred to as MCMF-MO-LSGDM, is explored in this study. Finally, the utility and superiority of the constructed model are confirmed through comparative analysis and simulation experiments against existing related works.
{"title":"A minimum cost and maximum fairness-driven multi-objective optimization consensus model for large-scale group decision-making","authors":"Yufeng Shen , Xueling Ma , Zeshui Xu , Muhammet Deveci , Jianming Zhan","doi":"10.1016/j.fss.2024.109198","DOIUrl":"10.1016/j.fss.2024.109198","url":null,"abstract":"<div><div>The rise of social media and e-democracy has driven a paradigm shift in decision-making, notably reflected in the changing ways of public participation and policymaking within decision-making processes. The increased focus on fairness and efficiency not only complicates the consensus-building process among diverse interests and perspectives, but also significantly adds to the complexity of decision-making and its implementation. In this context, balancing the interests of all parties while ensuring fairness and improving decision-making effectiveness becomes crucial. To address these challenges, this study develops a multi-objective optimization consensus framework for large-scale group decision-making (LSGDM) that integrates the interests of decision-makers (DMs) and a moderator, providing a more comprehensive tool. Specifically, this study first designs a DM weight determination method based on structural hole theory within fuzzy social networks. The proposed DM weight determination method effectively leverages the flexibility of fuzzy social networks and the comprehensiveness of structural hole theory to enhance the accuracy and reliability of weight assignment. Building on this, a novel clustering method based on the maximum group consensus level is developed, taking into account the varying importance of different DMs. Furthermore, a minimum cost and maximum fairness-driven multi-objective optimization LSGDM consensus model, referred to as MCMF-MO-LSGDM, is explored in this study. Finally, the utility and superiority of the constructed model are confirmed through comparative analysis and simulation experiments against existing related works.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"500 ","pages":"Article 109198"},"PeriodicalIF":3.2,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142703351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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