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Independent subcontexts and blocks of concept lattices. Definitions and relationships to decompose fuzzy contexts
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-02-28 DOI: 10.1016/j.fss.2025.109345
Roberto G. Aragón, Jesús Medina, Eloísa Ramírez-Poussa
{"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}
引用次数: 0
Solving on widest-interval solutions with the maximum width for a system of max-min fuzzy relational inequalities
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-02-28 DOI: 10.1016/j.fss.2025.109344
Zhen-Zhen Chen , Yan-Kuen Wu , Xiao-Ming Li , Meng-Li Zhu
{"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}
引用次数: 0
Discrete Laplace transform for interval-valued functions and its applications to interval fractional difference equations
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-02-27 DOI: 10.1016/j.fss.2025.109336
Xuelong Liu, Guoju Ye, Wei Liu
{"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}
引用次数: 0
Nonlinear approximation of vector-valued functions by Shepard operators based on max-product and max-min operations
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-02-27 DOI: 10.1016/j.fss.2025.109332
Oktay Duman , Esra Erkus-Duman
{"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}
引用次数: 0
Topological properties and structure of fuzzy star-shaped numbers in noncompact sets
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-02-26 DOI: 10.1016/j.fss.2025.109335
Wenjuan Liu , Dongming Liu
{"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}
引用次数: 0
Rational means, weak associativity of means, invariance with respect to mean-type and t-(norm,conorm) mappings and applications
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-02-25 DOI: 10.1016/j.fss.2025.109334
Anna Gołecka , Tomasz Małolepszy , Janusz Matkowski
{"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}
引用次数: 0
On representation and some properties of OFWA operators
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-02-25 DOI: 10.1016/j.fss.2025.109333
Radomír Halaš , Radko Mesiar , Jozef Pócs , Andrea Stupňanová
{"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}
引用次数: 0
Mean-squared exponential stabilization of Takagi-Sugeno fuzzy genetic oscillator networks involving switching control failures: A frame of spatio-temporal discretizations
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-02-24 DOI: 10.1016/j.fss.2025.109322
Sufang Han , Tianwei Zhang , Yanning Wang
{"title":"Mean-squared exponential stabilization of Takagi-Sugeno fuzzy genetic oscillator networks involving switching control failures: A frame of spatio-temporal discretizations","authors":"Sufang Han ,&nbsp;Tianwei Zhang ,&nbsp;Yanning Wang","doi":"10.1016/j.fss.2025.109322","DOIUrl":"10.1016/j.fss.2025.109322","url":null,"abstract":"<div><div>This article considers global asymptotic and exponential stabilizations in the mean-square sense of space-time discrete Takagi-Sugeno (T-S) fuzzy genetic oscillator networks (GONs) with switching actuator failures and Dirichlet controlled boundaries. It presents some exciting results for the criteria of global asymptotic stabilization in the mean-square sense for the proposed discrete T-S fuzzy GONs via the approaches of the Lyapunov-Krasovskii function, the discrete Wirtinger inequality, and the discrete formula of integration by parts. Besides, our research delves into the exciting possibility of global exponential stabilization in the mean-square sense, which offers a more comprehensive view of stabilized T-S fuzzy GONs than asymptotic stabilization. More critically, this study shows that global mean-square stabilizations of space-time discrete T-S fuzzy GONs can be achieved better by taking the values with the smaller diffusion intensities, smaller coupling strengths and bigger connection weights. Compared to the previous literatures, this paper offers a framework to discuss the issues of global stabilizations for space-time discrete T-S fuzzy GONs with switching actuator failures through the boundary controls, and the results are applicable in a wide range of applications. And finally, an illustrative example is presented to prove the method's validity.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"508 ","pages":"Article 109322"},"PeriodicalIF":3.2,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143480422","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}
引用次数: 0
The topological structures of the spaces of fuzzy numbers with the sendograph metric
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-02-21 DOI: 10.1016/j.fss.2025.109330
Wenjuan Liu , Zhongqiang Yang
{"title":"The topological structures of the spaces of fuzzy numbers with the sendograph metric","authors":"Wenjuan Liu ,&nbsp;Zhongqiang Yang","doi":"10.1016/j.fss.2025.109330","DOIUrl":"10.1016/j.fss.2025.109330","url":null,"abstract":"<div><div>For every non-degenerate convex subset <em>Y</em> of the <em>n</em>-dimensional Euclidean space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, let <span><math><mi>K</mi><mo>(</mo><mi>Y</mi><mo>)</mo></math></span> denote the set of all fuzzy numbers, which are fuzzy sets that are upper semi-continuous, fuzzy convex and normal with compact supports contained in <em>Y</em>. Consider the sendograph metric <span><math><msup><mrow><mi>D</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> defined on <span><math><mi>K</mi><mo>(</mo><mi>Y</mi><mo>)</mo></math></span>. Zhang has proven that <span><math><mo>(</mo><mi>K</mi><mo>(</mo><mi>Y</mi><mo>)</mo><mo>,</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></math></span> is homeomorphic to the separable Hilbert space <span><math><msup><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> when <em>Y</em> is compact or <span><math><mi>Y</mi><mo>=</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. In this paper, we show that <span><math><mo>(</mo><mi>K</mi><mo>(</mo><mi>Y</mi><mo>)</mo><mo>,</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></math></span> is homeomorphic to <span><math><msup><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> if and only if <em>Y</em> is topologically complete.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"508 ","pages":"Article 109330"},"PeriodicalIF":3.2,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474927","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}
引用次数: 0
Skill assessment method: A perspective from concept-cognitive learning
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-02-21 DOI: 10.1016/j.fss.2025.109331
Yin-Feng Zhou , Hai-Long Yang , Jin-Jin Li , Da-Li Wang
{"title":"Skill assessment method: A perspective from concept-cognitive learning","authors":"Yin-Feng Zhou ,&nbsp;Hai-Long Yang ,&nbsp;Jin-Jin Li ,&nbsp;Da-Li Wang","doi":"10.1016/j.fss.2025.109331","DOIUrl":"10.1016/j.fss.2025.109331","url":null,"abstract":"<div><div>Skills represent potential cognitive abilities that need to be reflected by observing external performances. In competence-based knowledge space theory, whether individuals solve items in a knowledge domain correctly can reflect whether they have mastered the relevant skills. Currently, skill function that reflects the relationship between skills and items has been extended to fuzzy skill function on polytomous items. However, existing skill assessment techniques are not suitable to assess response data that are noisy under the fuzzy skill function. Based on the fact that individuals' learning process of skills is consistent with the cognitive learning process, this paper provides a skill assessment method from a concept-cognitive learning perspective. A special fuzzy skill function, conjunctive fuzzy skill function, is converted into a fuzzy formal context. For facilitating skill assessment, the definitions of well-formed item-skill context and subsequent state are given. Based on a well-formed item-skill context and the idea of upper and lower approximations in rough set theory, the approximate concepts are learned by using response patterns as cues to provide a skill assessment method. The empirical application shows that the skill assessment method proposed in this paper is feasible and has practical applications.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"508 ","pages":"Article 109331"},"PeriodicalIF":3.2,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143480423","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}
引用次数: 0
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