Fuzzy Sets and Systems最新文献

{"title":"The weak dominance between t-norms and t-conorms revisited","authors":"Qiao-Yun Liu ,&nbsp;Feng Qin","doi":"10.1016/j.fss.2024.108988","DOIUrl":"https://doi.org/10.1016/j.fss.2024.108988","url":null,"abstract":"<div><p>The weak dominance relation between two binary operations was introduced as an extension of the dominance relation and the modularity equation. This paper continues the study of the weak dominance between t-norms and t-conorms. First, we present the characterization of the weak dominance of a nilpotent t-norm over a continuous Archimedean t-norm. Second, we establish the generalized sufficient and necessary conditions for the weak dominance of continuous t-norms over continuous t-norms. Finally, we obtain a generalized characterization of a continuous t-conorm weakly dominating a continuous t-norm by showing that <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>M</mi></mrow></msub></math></span> weakly dominates any t-norm.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140650388","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}

{"title":"Uncertainty measures and feature selection based on composite entropy for generalized multigranulation fuzzy neighborhood rough set","authors":"Xiaoyan Zhang,&nbsp;Weicheng Zhao","doi":"10.1016/j.fss.2024.108971","DOIUrl":"https://doi.org/10.1016/j.fss.2024.108971","url":null,"abstract":"<div><p>With the continuous advancement of information technology, the information and data covered by various information systems become increasingly complex and diverse, it is essential to perform knowledge mining from multiple perspectives to extract valuable insights. Fuzzy neighborhood multigranulation rough set, as an excellent feature selection model, is capable of handling heterogeneous datasets more effectively, significantly improving learning efficiency. In this study, we investigate a feature selection method based on a generalized multigranulation fuzzy rough set (GMFNRS) in fuzzy decision systems. First, the concepts of fuzzy neighborhood rough sets and generalized multigranulation rough sets are introduced. Subsequently, the GMFNRS model is established to enable data mining and rule extraction from various perspectives. Secondly, from an informational perspective, the study investigates uncertainty measurement methods through fuzzy neighborhood joint entropy. Furthermore, a novel fuzzy neighborhood generalized composite entropy is proposed by integrating the GMFNRS model with uncertainty measures. Finally, a forward greedy feature selection algorithm is considered to extract essential information from complex datasets. Experimental results on 15 public datasets demonstrate that the proposed model effectively selects important features in fuzzy systems and exhibits excellent classification performance.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140633068","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}

{"title":"Weights generation models based on acceptance degrees in decision making","authors":"LeSheng Jin ,&nbsp;Zhen-Song Chen ,&nbsp;Radko Mesiar ,&nbsp;Tapan Senapati ,&nbsp;Diego García-Zamora ,&nbsp;Luis Martínez","doi":"10.1016/j.fss.2024.108972","DOIUrl":"https://doi.org/10.1016/j.fss.2024.108972","url":null,"abstract":"<div><p>The process of determining weights for a collection of experts is an essential component in addressing collective decision-making issues. In cases where individual evaluation values are accompanied by uncertainties, it is feasible for each expert to endorse the evaluations of their peers without necessitating further interaction among the group. This study proposes innovative approaches to determining weights, primarily relying on measurements of the overall acceptance degree. Additionally, the guidelines for computing the total acceptance degrees are established. Various methods can be employed to derive and calculate the total acceptance degree of an expert based on the evaluations provided by other experts. The study at hand introduces several novel concepts, namely “parameterized family of uncertainty functions” and “uncertain system”, which can be effectively utilized for the development of relevant algorithms. The mathematical properties pertaining to the proposed concepts have been scrutinized and subsequently expounded upon. A normalized weight vector can be derived directly from any vector of the obtained total acceptance degrees. Numerical examples have been provided to serve the purpose of illustration and comparison.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140633069","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}

{"title":"The interactive fuzzy semigroup (RIC,+1/2) and its algebraic structure properties","authors":"Allan Edley Ramos de Andrade ,&nbsp;Vinícius Francisco Wasques","doi":"10.1016/j.fss.2024.108970","DOIUrl":"https://doi.org/10.1016/j.fss.2024.108970","url":null,"abstract":"<div><p>This paper studies algebraic properties of fuzzy numbers under a specific arithmetic operation denoted by <span><math><msub><mrow><mo>+</mo></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></math></span>. Specifically, this article establishes a new semigroup based on this sum and explores its algebraic properties, as well as homomorphisms between its subsemigroups. Some examples are provided in order to illustrate the results provided here.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140633067","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}

{"title":"Model checking fuzzy computation tree logic of multi-agent systems based on fuzzy interpreted systems","authors":"Zhanyou Ma,&nbsp;Xia Li,&nbsp;Ziyuan Liu,&nbsp;Ruiqi Huang,&nbsp;Nana He","doi":"10.1016/j.fss.2024.108966","DOIUrl":"https://doi.org/10.1016/j.fss.2024.108966","url":null,"abstract":"<div><p>Effective communication among autonomous agents is crucial for coordination and solving complex tasks within multi-agent systems. To formalize interactions between agents, social accessibility relations are often utilized. Current research employs model checking algorithms to verificate social commitment properties in multi-agent systems. In fuzzy multi-agent systems, direct quantification and computation of commitment attributes pose challenges. This paper introduces an indirect fuzzy model checking algorithm designed to convert social commitments in uncertain scenarios into quantifiable attributes for verification. Firstly, we propose a fuzzy communicative interpreted system model to represent multi-agent systems with uncertain communication. We then improve fuzzy computation tree logic by adding modalities for commitments and fulfillment, resulting in a fuzzy computation tree logic with commitments for describing system properties related to commitments. A fuzzy model checking algorithm is subsequently presented. This algorithm converts the task of model checking fuzzy computation tree logic with commitments based on fuzzy interpreted systems into model checking fuzzy computation tree logic based on fuzzy Kripke structures. We conclude by providing proofs of correctness and complexity analysis of our algorithm. Furthermore, we demonstrate the effectiveness of our approach for model checking social commitments under fuzzy conditions through simulation experiments on an online shopping system.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140546341","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}

{"title":"Explicit formulas for t-conorms constructed by the sum of ranges of discrete additive generators of t-conorms","authors":"Peter Viceník","doi":"10.1016/j.fss.2024.108968","DOIUrl":"https://doi.org/10.1016/j.fss.2024.108968","url":null,"abstract":"<div><p>Explicit formulas for t-conorms constructed by the sum of ranges of discrete additive generators of t-conorms are introduced.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140543287","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}

{"title":"Updating information based on generalized credal sets. Part 2: General case","authors":"Andrey G. Bronevich ,&nbsp;Igor N. Rozenberg","doi":"10.1016/j.fss.2024.108967","DOIUrl":"https://doi.org/10.1016/j.fss.2024.108967","url":null,"abstract":"<div><p>In the first part of this paper, we have considered: a) generalized credal sets on the powerset of a finite set <em>X</em>; b) their general definition allowing a generalized credal set to be not convex; c) the justification of basic aggregation rules on generalized credal sets; d) ways of updating information. The second part is devoted to the solutions of the above problems for the general case, when generalized credal sets are defined on arbitrary measurable spaces. In addition, we prove that the conditionals after updating of a generalized credal set could be chosen ratio-equivalent. This result confirms the thesis by R.A. Fisher, which says that the likelihood function is defined uniquely up to a positive coefficient.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140543286","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}

{"title":"Augmentation of degranulation mechanism for high-dimensional data with a multi-round optimization strategy","authors":"Xiaoan Tang ,&nbsp;Mingsong Duan ,&nbsp;Kaijie Xu ,&nbsp;Qiang Zhang","doi":"10.1016/j.fss.2024.108969","DOIUrl":"https://doi.org/10.1016/j.fss.2024.108969","url":null,"abstract":"<div><p>Various fuzzy clustering-based granulation–degranulation techniques have been developed for constructing and optimizing information granules, which help reveal the underlying structure of experimental data in Granular Computing (GrC). Basically, a well-performing granulation–degranulation mechanism runs with a low degranulation (reconstruction) error. However, the increasingly high-dimensional characteristics of data bring great challenges to achieve accurate of reconstruction of high-dimensional data. As such, for the reconstruction of high-dimensional data, an important issue is how to reduce the reconstruction error such that the data could be reconstructed more accurately. In order to address the challenge of unacceptable high reconstruction error posed by the increase in data dimensions and improve the inefficient fuzzy clustering-based granulation in existing techniques, this study develops a multi-round iterative optimization strategy with the use of Fuzzy C-Means (FCM) to enhance reconstruction performance for high-dimensional data. First, we propose a Feature Sampling-based FCM (FS-FCM) scheme served as the granulation mechanism in the framework. The proposed scheme draws on the idea of ensemble learning, where the granulation of original high-dimensional data is accomplished by generating and training low-dimensional sub-datasets through multiple times of feature random sampling. Then, a multi-round iterative granulation–degranulation mechanism is proposed along with its algorithmic framework. Within the proposed framework, we attempt to reduce the reconstruction error by iteratively reconstructing the residual data generated in each round of granulation–degranulation. Finally, we validate the developed strategy framework over twelve publicly available datasets with varying dimension scales. A set of ablation experiments verifies the effectiveness of the FS-FCM granulation scheme. The near-perfect reconstruction performance achieved by the proposed iterative framework on the given datasets further demonstrates its superiority.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140606932","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}

{"title":"Pseudo-moment generating functions: Application to pseudo-Schur constant random vectors","authors":"Sabrina Mulinacci,&nbsp;Massimo Ricci","doi":"10.1016/j.fss.2024.108963","DOIUrl":"https://doi.org/10.1016/j.fss.2024.108963","url":null,"abstract":"<div><p>In this note we show that pseudo-analysis tools can be effective in obtaining results in a distorted probability framework. More precisely, we introduce the notion of pseudo-independence and that of pseudo-moment generating function, the latter representing a generalization of the pseudo-Laplace transform, and both aiming at extending the corresponding notions in the usual probabilistic context. We show that these concepts and their properties, and more in general pseudo-analysis, are particularly useful to provide characterization results for a class of bivariate random vectors that we call “pseudo-Schur constant” family which represents an extension of the Schur-constant class.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S016501142400109X/pdfft?md5=2e260f004ae5fa96086cc4b6e4a33a0a&pid=1-s2.0-S016501142400109X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140349869","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}

{"title":"A unified framework of fuzzy implications and coimplications","authors":"Yifan Zhao,&nbsp;Hua-Wen Liu","doi":"10.1016/j.fss.2024.108962","DOIUrl":"10.1016/j.fss.2024.108962","url":null,"abstract":"<div><p>Fuzzy implications and coimplications play important roles in both theoretic and applied communities of fuzzy set theory. In this paper, we provide a unified framework for fuzzy implications and coimplications. Specifically, firstly, we introduce the concept of uni-implications, which is the unification of fuzzy implications and coimplications, and describe the structure of uni-implications. Secondly, we discuss the relationships among uni-implications, fuzzy boundary weak implications and fuzzy (co)implications. Thirdly, we present two constructions and equivalent characterizations of non-trivial uni-implications, respectively. Finally, we propose two binary operations <span><math><mo>♠</mo><mo>,</mo><mo>♡</mo></math></span> on some subset of the set of non-trivial uni-implications, denoted by <span><math><msub><mrow><mi>F</mi></mrow><mrow><mtext>SNT</mtext></mrow></msub></math></span>, which make <span><math><mo>(</mo><msub><mrow><mi>F</mi></mrow><mrow><mtext>SNT</mtext></mrow></msub><mo>,</mo><mo>♠</mo><mo>)</mo></math></span> a semigroup and <span><math><mo>(</mo><msub><mrow><mi>F</mi></mrow><mrow><mtext>SNT</mtext></mrow></msub><mo>,</mo><mo>♡</mo><mo>)</mo></math></span> a non-commutative and non-idempotent monoid.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140405976","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}