Fuzzy Sets and Systems最新文献

{"title":"How to tractably compute a productive repair for possibilistic partially ordered DL-LiteR ontologies?","authors":"Ahmed Laouar ,&nbsp;Sihem Belabbes ,&nbsp;Salem Benferhat","doi":"10.1016/j.fss.2025.109361","DOIUrl":"10.1016/j.fss.2025.109361","url":null,"abstract":"<div><div>The lightweight description logic dialect DL-Lite<span><math><msub><mrow></mrow><mrow><mi>R</mi></mrow></msub></math></span> offers a framework for specifying and reasoning with formal inconsistent ontologies. Basically, an ontology is a knowledge base composed of a TBox, modelling conceptual knowledge of some domain of interest, and an ABox, asserting factual knowledge about specific entities of the domain. Inconsistency in an ontology is usually handled by evaluating queries over maximal conflict-free subsets of the ABox, called data repairs. Several inconsistency-tolerant semantics, with different levels of cautiousness and computational cost, propose strategies for selecting the repairs to consider when deriving new conclusions from an inconsistent ontology. In this paper, we focus on partially ordered ontologies where a partial order relation captures the reliability levels of the ABox elements. We propose a new tractable method, called “C<em>π</em>-repair”, which leverages possibility theory in repairing a partially ordered ABox. It proceeds in four steps as follows. First, the partial order relation is extended into a family of total orders, thus inducing as many compatible totally ordered ABoxes. Second, a single repair is computed for each compatible ABox. Third, these repairs are closed deductively in order to improve their productivity, i.e., to derive more facts. Finally, the closed repairs are intersected to produce a single repair for the initial partially ordered ABox. The main contribution of this paper is an equivalent characterization that determines the validity of the conclusions drawn with the “C<em>π</em>-repair” method, but without eliciting the compatible ABoxes or computing their repairs. This allows us to establish the tractability of the method by reformulating the problem using the notions of support for an assertion and dominance over the conflicts that arise between the ABox elements. Essentially, the valid conclusions are those derived from the supports that dominate all conflicts. In the last part of the paper, we explore the rationality properties of our method. We show that increasing repair productivity does not alter the satisfaction of the rationality properties. We also discuss the applicability of our proposed method to languages richer than DL-Lite<span><math><msub><mrow></mrow><mrow><mi>R</mi></mrow></msub></math></span> and to other inconsistency-tolerant semantics.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"510 ","pages":"Article 109361"},"PeriodicalIF":3.2,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143562519","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":"Labeled Fuzzy Reactive Graphs","authors":"Suene Campos ,&nbsp;Daniel Figueiredo ,&nbsp;Manuel A. Martins ,&nbsp;Regivan Santiago","doi":"10.1016/j.fss.2025.109320","DOIUrl":"10.1016/j.fss.2025.109320","url":null,"abstract":"<div><div>The topic of fuzzy and relation-changing structures have been progressively explored through the authors' previous work. This paper continues to expand the range of application for these models by introducing Labeled Fuzzy Reactive Graphs. This structure admits labels in regular edges, in order to permit to describe the action of different agents. For such structures, the operations of union, intersection and threshold are presented. Subsequently, this structure is applied to model a cancer treatment protocol and it is shown how the relation-changing properties of this structure can be used to better describe the dynamics of the modelled protocol.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"510 ","pages":"Article 109320"},"PeriodicalIF":3.2,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143562518","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":"Fuzzification of crisp functions using gradual elements and gradual sets","authors":"Hsien-Chung Wu","doi":"10.1016/j.fss.2025.109358","DOIUrl":"10.1016/j.fss.2025.109358","url":null,"abstract":"<div><div>There are two ways to fuzzify the crisp functions into fuzzy functions. One is using the extension principle. Another one is using the expression in decomposition theorem. In this paper, we present a new methodology to fuzzify the crisp functions for non-normal fuzzy sets using the concepts of gradual elements and gradual sets. The main purpose of this paper is to establish the equivalence between the fuzzy functions that are obtained using the extension principle and the gradual elements when the membership functions are assumed to be upper semi-continuous. This kind of technique is based on the idea in which the fuzzy set is formulated as consisting of gradual elements like the usual set consisting of usual elements. In this case, the operations among sets can be borrowed to set up the operations among fuzzy sets.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"509 ","pages":"Article 109358"},"PeriodicalIF":3.2,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552808","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":"Independent subcontexts and blocks of concept lattices. Definitions and relationships to decompose fuzzy contexts","authors":"Roberto G. Aragón,&nbsp;Jesús Medina,&nbsp;Eloísa Ramírez-Poussa","doi":"10.1016/j.fss.2025.109345","DOIUrl":"10.1016/j.fss.2025.109345","url":null,"abstract":"<div><div>The decomposition of datasets is a useful mechanism in the processing of large datasets and it is required in many cases. In formal concept analysis (FCA), the dataset is interpreted as a context and the notion of independent context is relevant in the decomposition of a context. In this paper, we have introduced a formal definition of independent context within the multi-adjoint concept lattice framework, which can be translated to other fuzzy approaches. Furthermore, we have analyzed the decomposition of a general bounded lattice in pieces, that we have called blocks. This decomposition of a lattice has been related to the existence of a decomposition of a context into independent subcontexts. This study will allow to develop algorithms to decompose datasets with imperfect information.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"509 ","pages":"Article 109345"},"PeriodicalIF":3.2,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552810","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":"Solving on widest-interval solutions with the maximum width for a system of max-min fuzzy relational inequalities","authors":"Zhen-Zhen Chen ,&nbsp;Yan-Kuen Wu ,&nbsp;Xiao-Ming Li ,&nbsp;Meng-Li Zhu","doi":"10.1016/j.fss.2025.109344","DOIUrl":"10.1016/j.fss.2025.109344","url":null,"abstract":"<div><div>The system of max-min fuzzy relational inequalities (FRI) was established to model the problems of instructional information resource allocation and peer-to-peer file-sharing systems. Considering the instability and fragility of the optimal solution, researchers design the widest-interval solution of the max-min FRI to allow the solution to fluctuate within a certain range. As a result, there are still numerous, or even infinite, widest-interval solutions in the system. To better demonstrate the differences among the various widest-interval solutions, this paper proposes the widest-interval solutions with the maximum width for the system. The widest-interval solutions with the maximum width, as its name indicates, have the largest interval width compared to other solutions. Consequently, it can contribute to the robust solution and stable system behavior. Built upon new theoretical insights, a novel solution method is developed to obtain widest-interval solutions with the maximum width. A numerical illustration is presented to demonstrate the detailed procedure of this method.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"509 ","pages":"Article 109344"},"PeriodicalIF":3.2,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552809","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":"Discrete Laplace transform for interval-valued functions and its applications to interval fractional difference equations","authors":"Xuelong Liu,&nbsp;Guoju Ye,&nbsp;Wei Liu","doi":"10.1016/j.fss.2025.109336","DOIUrl":"10.1016/j.fss.2025.109336","url":null,"abstract":"<div><div>This work aims to present a discrete Laplace transform for handling interval fractional difference equations. We first deal with algebraic properties of the forward gH-difference operator for interval-valued functions. In particular, the forward gH-difference operator of the product of a real function and an interval-valued function is studied, which is then applied to establish summation by parts of interval-valued functions. Moreover, we present the new concept of discrete Laplace transform for interval-valued functions and study some relevant properties. The discrete Laplace transform formula on forward gH-difference operators is derived by applying summation by parts. Finally, the analytic solution of the interval Caputo fractional difference equations is established by means of the discrete Laplace transform. The results developed in this paper are illustrated through several numerical examples.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"509 ","pages":"Article 109336"},"PeriodicalIF":3.2,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143520748","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":"Nonlinear approximation of vector-valued functions by Shepard operators based on max-product and max-min operations","authors":"Oktay Duman ,&nbsp;Esra Erkus-Duman","doi":"10.1016/j.fss.2025.109332","DOIUrl":"10.1016/j.fss.2025.109332","url":null,"abstract":"<div><div>In this paper, to approximate vector-valued and continuous functions on the unit hypercube, we modify the linear Shepard operators by using max-product and max-min operations. We also investigate the effects of some regular summability methods in the approximation, such as Cesàro summability and Abel summability. Furthermore, we give some interesting applications and graphical simulations verifying our theoretical results. For example, we approximate a torus surface, a helix curve, a fuzzy point and the LogSumExp function by means of these modified operators. Our applications show that the results obtained here are connected with not only the classical approximation theory but also the theory of fuzzy logic and machine learning algorithms.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"509 ","pages":"Article 109332"},"PeriodicalIF":3.2,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143528693","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":"Topological properties and structure of fuzzy star-shaped numbers in noncompact sets","authors":"Wenjuan Liu ,&nbsp;Dongming Liu","doi":"10.1016/j.fss.2025.109335","DOIUrl":"10.1016/j.fss.2025.109335","url":null,"abstract":"<div><div>Fuzzy star-shaped numbers, serving as a fuzzy extension of star-shaped sets, occupy a pivotal position within the framework of fuzzy number theory. In our previous research, we have established the fact that the space of fuzzy star-shaped numbers equipped with the sendograph metric is homeomorphic to the separable Hilbert space if the base space is compact. In this current work, we further investigate the topological properties and structure of the space of fuzzy star-shaped numbers when the base space is noncompact.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"509 ","pages":"Article 109335"},"PeriodicalIF":3.2,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143528888","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":"Rational means, weak associativity of means, invariance with respect to mean-type and t-(norm,conorm) mappings and applications","authors":"Anna Gołecka ,&nbsp;Tomasz Małolepszy ,&nbsp;Janusz Matkowski","doi":"10.1016/j.fss.2025.109334","DOIUrl":"10.1016/j.fss.2025.109334","url":null,"abstract":"<div><div>The means and <em>t</em>-norms are considered. A weak associativity property of the weighted quasi-arithmetic means, connecting these two families of functions, is introduced. It is observed that the symmetry of every <em>t</em>-norm follows from a modified system of the remaining axioms. The conditions under which a rational function is a bivariate homogeneous mean in <span><math><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span> are given. The invariance of means and functions with respect to the mean-type mappings and <em>t</em>-(norm,conorm)-type mappings is considered with some applications.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"508 ","pages":"Article 109334"},"PeriodicalIF":3.2,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510397","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 representation and some properties of OFWA operators","authors":"Radomír Halaš ,&nbsp;Radko Mesiar ,&nbsp;Jozef Pócs ,&nbsp;Andrea Stupňanová","doi":"10.1016/j.fss.2025.109333","DOIUrl":"10.1016/j.fss.2025.109333","url":null,"abstract":"<div><div>Ordered functional weighted averaging operators (OFWA operators) represent a generalization of OWA operators that are commonly used in decision making. It is shown that the class of OFWA operators is identical to the class of all intermediate functions, i.e. functions between min and max. The involved representation of OFWA operators determines a mapping between the set of all functions defined on the unit real interval and the family of all intermediate functions. The aim of this paper is to study some properties of this representation, in particular from a topological and algebraic point of view.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"508 ","pages":"Article 109333"},"PeriodicalIF":3.2,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510398","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}