Fuzzy Sets and Systems最新文献

{"title":"Tri-composed fuzzy relation inequality with weighted-max-min composition and the relevant min-max optimization problem","authors":"Zhining Wang ,&nbsp;Guocheng Zhu ,&nbsp;Xiaopeng Yang","doi":"10.1016/j.fss.2024.109011","DOIUrl":"10.1016/j.fss.2024.109011","url":null,"abstract":"<div><p>In the existing works, the classical fuzzy relation inequality (FRI) with double-composed operators has been introduced to describe the P2P network system. In this work, considering the successful rate of the line connection within the P2P network system, we establish the so-called tri-composed FRI, with a weighted-max-min composition, for the first time. We study the solutions induced through paths and further construct the complete solution set of the tri-composed FRI using the path-induced solutions. Moreover, the whole solution set could be fully determined by all the path-induced solutions and its unique maximum solution. Furthermore, considering a specific optimal management objective in the P2P network, we further study the min-max optimization problem with the tri-composed FRI constraints. A path-based algorithm is proposed for handling the problem we studied, accompanied by an illustrative example.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141022812","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":"On linear combinations of binomial OWA functions","authors":"Silvia Bortot,&nbsp;Ricardo Alberto Marques Pereira","doi":"10.1016/j.fss.2024.109010","DOIUrl":"10.1016/j.fss.2024.109010","url":null,"abstract":"<div><p>We consider the binomial decomposition of ordered weighted averaging (OWA) functions proposed by Calvo and De Baets (1998) in the framework of Choquet integration. Our aim in the paper is to further investigate the equivalence between the two representations of OWA functions involved in the binomial decomposition: the usual canonical representation in terms of the order statistics, and the binomial representation in terms of the binomial OWA functions. We describe and discuss in detail the linear transformations that relate the coefficients of these two equivalent representations: the original expression of the weights in terms of the coefficients of the binomial representation, and its inverse, the expression of those coefficients in terms of the weights. In both cases simple and direct proofs are presented. Moreover, we consider the linear transformations between the two representations in the general linear algebra framework of unconstrained linear combinations of binomial OWA functions. In this perspective we obtain compact matrix expressions for the linear transformations, which also offer new insight on the geometry of the coefficient constraints in the binomial representation of OWA functions.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0165011424001568/pdfft?md5=d750876ce0c7e05fdbd0625a9183664f&pid=1-s2.0-S0165011424001568-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141061835","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":"Generalized extended Bonferroni means for isomorphic membership grades","authors":"Zhen-Song Chen ,&nbsp;Yi Yang ,&nbsp;LeSheng Jin ,&nbsp;Bapi Dutta ,&nbsp;Luis Martínez ,&nbsp;Witold Pedrycz ,&nbsp;Radko Mesiar ,&nbsp;Humberto Bustince","doi":"10.1016/j.fss.2024.109009","DOIUrl":"10.1016/j.fss.2024.109009","url":null,"abstract":"<div><p>The generalized extended Bonferroni mean (GEBM) is a powerful tool for modeling the complex process of aggregating information, whether it is homogeneously or heterogeneously connected, within a composite aggregation structure. It maintains several favorable characteristics and effectively captures the diverse and interconnected nature of expert opinions or criteria, which is commonly observed in various decision-making contexts. This research expands upon the existing GEBM framework by applying it to the specific domains of q-rung orthopair fuzzy sets (<em>q</em>-ROFSs) and extended <em>q</em>-rung orthopair fuzzy sets (E<em>q</em>-ROFSs). Furthermore, it examines the transformation processes among different variants of GEBMs. To facilitate the development of generalized aggregation functions, the de Morgan triplets for <em>q</em>-ROFSs and E<em>q</em>-ROFSs are established. By introducing an isomorphism, the transformation relationship between the aggregation functions for <em>q</em>-ROFSs and E<em>q</em>-ROFSs is analyzed. Based on this foundation, the Bonferroni mean de Morgan triplet-based GEBMs for <em>q</em>-ROFSs and E<em>q</em>-ROFSs are proposed, and the keeping-order relations for these proposed GEBMs are discussed. Finally, several special cases of the GEBMs for <em>q</em>-ROFSs and E<em>q</em>-ROFSs are obtained, and several relevant theorems are verified.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141041585","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":"EFNN-Nul0- a trustworthy knowledge extraction about stress identification through evolving fuzzy neural networks","authors":"Paulo Vitor de Campos Souza,&nbsp;Mauro Dragoni","doi":"10.1016/j.fss.2024.109008","DOIUrl":"https://doi.org/10.1016/j.fss.2024.109008","url":null,"abstract":"<div><p>This paper presents a novel hybrid architecture, denoted as <em>EFNN-Nul0</em> (evolving neuro-fuzzy system based on null-unineurons), meticulously crafted for stress identification within the realm of pattern classification. The model seamlessly integrates neural networks, fuzzy systems, and n-uninorms to cultivate knowledge within an adaptive, real-time learning context. Neuro-fuzzy rules, encapsulating interdependencies among input features through IF-THEN type relationships, are formulated utilizing null-unineurons derived from n-uninorms. This construction enables the articulation of both AND- and OR-connections, thereby augmenting the interpretability of the generated rules. The evolution of neurons is facilitated by an extended adaptation of the autonomous data partition method (ADPA). To dynamically interpret the evolution of rules, the paper introduces (i) a mechanism that tracks changes in rules over data stream samples, providing insights into the process dynamics as a structural active learning component, and (ii) a concept for incrementally updating feature weights. These weights encapsulate the varying impact levels of features on stress identification, enabling the reduction of rule length by effectively masking out less significant features. The outcomes of the rules are represented by certainty vectors, recursively updated through an indicator-based recursive weighted least squares (I-RWLS) approach. Neuron activation levels play a pivotal role in determining the weights, ensuring stable local learning. The effectiveness of the proposed model is substantiated through a comprehensive comparison with existing hybrid and evolving approaches in the literature, focusing on binary and multi-class pattern classification. Aspects that identify special characteristics of neuro-fuzzy models related to interpretability will also be demonstrated in this work. The results demonstrate the model's superior performance, characterized by consistently higher accuracy trend lines over time. Furthermore, the model's interpretability is underscored by the coherent neuro-fuzzy rules, contributing to its remarkable accuracy (the EFNN-Nul0 achieved approximately 99% accuracy in stress identification), establishing its efficacy in addressing stress identification within classification problems.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140947618","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":"On the lattice of fuzzy rough sets","authors":"Dávid Gégény ,&nbsp;Sándor Radeleczki","doi":"10.1016/j.fss.2024.108999","DOIUrl":"10.1016/j.fss.2024.108999","url":null,"abstract":"<div><p>By the means of lower and upper fuzzy approximations we define quasiorders. Their properties are used to prove our main results. First, we characterize the pairs of fuzzy sets that form fuzzy rough sets w.r.t. a t-similarity relation <em>θ</em> on <em>U</em>, for certain t-norms and implicators. If <em>U</em> is finite or the range of <em>θ</em> and of the fuzzy sets is a fixed finite chain, we establish conditions under which fuzzy rough sets form lattices. We show that this is the case for the min t-norm and any S-implicator defined by an involutive negator and the max co-norm.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0165011424001453/pdfft?md5=369560d5ac8e86abf971d5a184d9b22d&pid=1-s2.0-S0165011424001453-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141044999","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":"Fuzzification using the extension principle and the expression in decomposition theorem","authors":"Hsien-Chung Wu","doi":"10.1016/j.fss.2024.109000","DOIUrl":"https://doi.org/10.1016/j.fss.2024.109000","url":null,"abstract":"<div><p>Fuzzifying the crisp functions is a well-known methodology to study the problems under fuzzy uncertainty. The traditional way for fuzzifying the crisp functions is based on the extension principle. In this paper, by referring to the expression in decomposition theorem, we present a new methodology to fuzzify the crisp functions for non-normal fuzzy sets. The main purpose of this paper is to establish the equivalence between the fuzzy functions obtained from the extension principle and the expression in decomposition theorem under the proposed concept of compatibility. The practical cases regarding the equivalences are also studied in order to be used for the practical problems.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140901145","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":"On the general fractal dimensions of hyperspace of compact sets","authors":"Dandan Cheng ,&nbsp;Zhiming Li ,&nbsp;Bilel Selmi","doi":"10.1016/j.fss.2024.108998","DOIUrl":"10.1016/j.fss.2024.108998","url":null,"abstract":"<div><p>Consider a separable metric space <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>d</mi><mo>)</mo></math></span>, and let <span><math><mo>(</mo><mi>K</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>,</mo><mover><mrow><mi>d</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>)</mo></math></span> denote the space of non-empty compact subsets of <em>X</em> equipped with the Hausdorff metric. This paper aims to introduce and investigate the concepts of two general fractal dimensions and general dimensions within the framework of <span><math><mo>(</mo><mi>K</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>,</mo><mover><mrow><mi>d</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>)</mo></math></span>. In particular, we explore a relationship between the general fractal dimensions of a set <em>Z</em> of a self-similar sequence space and their counterparts in the space of compact subsets <span><math><mi>K</mi><mo>(</mo><mi>Z</mi><mo>)</mo></math></span>.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140931034","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 general algebraic solution of dual fuzzy linear systems and fuzzy Stein matrix equations","authors":"Đorđe Dragić,&nbsp;Biljana Mihailović,&nbsp;Ljubo Nedović","doi":"10.1016/j.fss.2024.108997","DOIUrl":"https://doi.org/10.1016/j.fss.2024.108997","url":null,"abstract":"<div><p>In this paper, we present a new method for solving a dual fuzzy linear system (DFLS), <span><math><mi>A</mi><mover><mrow><mi>X</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>+</mo><mover><mrow><mi>C</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>=</mo><mi>B</mi><mover><mrow><mi>X</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>+</mo><mover><mrow><mi>D</mi></mrow><mrow><mo>˜</mo></mrow></mover></math></span>, where the coefficient matrices <em>A</em> and <em>B</em> are arbitrary real <span><math><mi>m</mi><mo>×</mo><mi>n</mi></math></span> matrices and <span><math><mover><mrow><mi>C</mi></mrow><mrow><mo>˜</mo></mrow></mover></math></span> and <span><math><mover><mrow><mi>D</mi></mrow><mrow><mo>˜</mo></mrow></mover></math></span> are given fuzzy number vectors. A necessary and sufficient condition for the <span><math><mi>R</mi></math></span>-consistency of the associated system of linear equations is obtained. The straightforward method for solving <span><math><mi>m</mi><mo>×</mo><mi>n</mi></math></span> DFLS based on an arbitrary {1}-inverse of <span><math><mi>A</mi><mo>−</mo><mi>B</mi></math></span> is introduced. Also, as an application, we present the first algorithm for solving the fuzzy Stein matrix equations, based on {1}-inverses. Finally, these results are illustrated by examples.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140905476","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":"A Radon-Nikodym theorem for monotone measures","authors":"Yao Ouyang ,&nbsp;Jun Li","doi":"10.1016/j.fss.2024.108995","DOIUrl":"https://doi.org/10.1016/j.fss.2024.108995","url":null,"abstract":"<div><p>A version of Radon-Nikodym theorem for the Choquet integral w.r.t. monotone measures is proved. Without any presumptive condition, we obtain a necessary and sufficient condition for the ordered pair <span><math><mo>(</mo><mi>μ</mi><mo>,</mo><mi>ν</mi><mo>)</mo></math></span> of finite monotone measures to have the so-called Radon-Nikodym property related to a nonnegative measurable function <em>f</em>. If <em>ν</em> is null-continuous and weakly null-additive, then <em>f</em> is uniquely determined almost everywhere by <em>ν</em> and thus is called the Radon-Nikodym derivative of <em>μ</em> w.r.t. <em>ν</em>. For <em>σ</em>-finite monotone measures, a Radon-Nikodym type theorem is also obtained under the assumption that the monotone measures are lower continuous and null-additive.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140843661","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":"Dissipative control for quaternion-valued fuzzy memristive neural networks: Nonlinear scalarization approach","authors":"Hongzhi Wei ,&nbsp;Hongjun Zhou ,&nbsp;Ruoxia Li ,&nbsp;Ning Li","doi":"10.1016/j.fss.2024.108996","DOIUrl":"https://doi.org/10.1016/j.fss.2024.108996","url":null,"abstract":"<div><p>This paper deals with the dissipative control for a class of quaternion-valued fuzzy memristive neural networks. By constructing proper Lyapunov functionals and using adaptive controller, the strictly <span><math><mo>(</mo><mi>Q</mi><mo>,</mo><mi>S</mi><mo>,</mo><mi>R</mi><mo>)</mo></math></span>-dissipative are characterized parametrically. Then, based on the algebraic inequality and linear matrix inequality (LMI) approach, sufficient conditions for the existence of the dissipative controllers are obtained. In addition, the nonlinear scalarization approach is developed, which can be employed to compare the “size” of two different quaternions, in this way, the convex closure proposed by the quaternion weights are meaningful. Finally, simulation examples are given to show the efficiency of the proposed methods.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140842874","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}