Fuzzy Sets and Systems最新文献

{"title":"An improved control law for TS fuzzy models: Less conservative LMI conditions by using membership functions derivative","authors":"Leonardo Amaral Mozelli,&nbsp;Victor Costa da Silva Campos","doi":"10.1016/j.fss.2025.109455","DOIUrl":"10.1016/j.fss.2025.109455","url":null,"abstract":"<div><div>This note proposes an enhanced version of the Parallel Distributed Compensation (PDC) for Takagi-Sugeno (TS) fuzzy models. Our approach involves two control terms based on state feedback. The first term is a convex combination of linear gains weighted by the normalized membership grade, as in traditional PDC. The second term is the main contribution and introduces linear gains weighted by the time derivatives of the membership functions. We formulate the design conditions as Linear Matrix Inequalities (LMIs), solvable through numerical optimization tools. Numerical examples illustrate the advantages of our proposal, which encompasses the traditional PDC as a special case.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"517 ","pages":"Article 109455"},"PeriodicalIF":3.2,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144068359","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":"Probabilistic linguistic three-way decisions: Integrating prospect theory with fuzzy possibilistic C-means clustering","authors":"Xiaoyan Zhang,&nbsp;Feiyu Liu","doi":"10.1016/j.fss.2025.109442","DOIUrl":"10.1016/j.fss.2025.109442","url":null,"abstract":"<div><div>This study proposes a novel multi-attribute decision-making (MADM) approach, Probabilistic Linguistic Three-Way Decision with Prospect Theory (PL-TWDP), which integrates Prospect Theory (PT) into the framework of Probabilistic Linguistic Term Sets (PLTSs). The method introduces an innovative technique for determining attribute weights by combining information entropy and deviation from the negative ideal solution (NIS), and develops a group satisfaction index to address limitations of traditional utility functions. The Fuzzy Possibilistic C-Means (FPCM) clustering algorithm is extended to refine the evaluation matrix in PLTSs, enhancing the identification of equivalent objects across clusters and the computation of conditional probabilities within the Three-Way Decision (TWD) model. By incorporating PT, the PL-TWDP method ranks alternatives based on utility perception values, promoting objective decision-making in probabilistic linguistic contexts. The effectiveness and superiority of the PL-TWDP method are demonstrated through a case study on air quality evaluation across multiple regions in China. Compared with eight established MADM methods, the proposed approach shows significant improvements in classification accuracy and robustness. Sensitivity analysis confirms its stability under varying parameter settings. This method effectively addresses uncertainties and risks in complex decision environments, providing a practical and reliable decision-making tool. Future work will focus on extending the method to handle large-scale group decision-making scenarios and further refining the integration of PT with PLTSs to enhance decision-making efficiency and accuracy.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"517 ","pages":"Article 109442"},"PeriodicalIF":3.2,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144068360","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":"Uniform random fuzzy measures","authors":"Juan Baz ,&nbsp;Gleb Beliakov ,&nbsp;Irene Díaz ,&nbsp;Susana Montes","doi":"10.1016/j.fss.2025.109447","DOIUrl":"10.1016/j.fss.2025.109447","url":null,"abstract":"<div><div>Random generation of fuzzy measures is an important computational task in applied problems related to fuzzy integrals such as the Choquet, Sugeno or Shilkret integrals. In general, a desirable property is the uniformity over the set of fuzzy measures. However, testing this property is not an easy task. In this paper, properties of uniform random fuzzy measures are derived. Special attention is being paid to the families of balanced fuzzy measures, belief measures and possibilities measures. Then, based of such properties, statistical tests for the uniformity of random fuzzy measures are developed. Finally, the uniformity of the most used algorithms is tested using the proposed methods.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"516 ","pages":"Article 109447"},"PeriodicalIF":3.2,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143948326","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 characterization of general pseudo-homogeneous t-norms","authors":"Feng-qing Zhu ,&nbsp;Xue-ping Wang","doi":"10.1016/j.fss.2025.109459","DOIUrl":"10.1016/j.fss.2025.109459","url":null,"abstract":"<div><div>This article first introduces the concept of a general pseudo-homogeneous triangular norm. It then gives some properties of general pseudo-homogeneous triangular norms. Finally, it characterizes all general pseudo-homogeneous triangular norms completely.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"517 ","pages":"Article 109459"},"PeriodicalIF":3.2,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144068358","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":"n-ary associative functions","authors":"Zhi-qiang Lai,&nbsp;Xue-ping Wang","doi":"10.1016/j.fss.2025.109446","DOIUrl":"10.1016/j.fss.2025.109446","url":null,"abstract":"<div><div>Let <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>⁎</mo></mrow></msup><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> be an associative function with neutral element, <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><mn>1</mn><mo>]</mo></math></span> be a monotone right continuous function 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><mn>1</mn><mo>]</mo><mo>→</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> be the pseudo-inverse of <em>f</em>. This article answers the question: what properties of the range of a generator <em>f</em> are sufficient and necessary for the corresponding generated 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><msup><mrow><mi>T</mi></mrow><mrow><mo>⁎</mo></mrow></msup><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> with property of <span><math><mi>T</mi><mo>(</mo><mo>⋯</mo><mi>T</mi><mo>(</mo><mi>T</mi><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>)</mo><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo><mo>=</mo><msup><mrow><mi>f</mi></mrow><mrow><mo>(</mo><mo>−</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>(</mo><msup><mrow><mi>T</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>f</mi><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo><mo>,</mo><mo>⋯</mo><mo>,</mo><mi>f</mi><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo><mo>)</mo><mo>)</mo></math></span> for all <span><math><mi>n</mi><mo>∈</mo><mo>{</mo><mn>1</mn><mo>,</mo><mo>⋯</mo><mo>,</mo><mi>n</mi><mo>,</mo><mo>⋯</mo><mo>}</mo></math></span> with <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span> and for all <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"516 ","pages":"Article 109446"},"PeriodicalIF":3.2,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143948327","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 relationships between type-2 t-norms on normal convex fuzzy truth values","authors":"Wei Zhang ,&nbsp;Bao Qing Hu ,&nbsp;Xinxing Wu","doi":"10.1016/j.fss.2025.109445","DOIUrl":"10.1016/j.fss.2025.109445","url":null,"abstract":"<div><div>Recent literature has mainly focused on four forms of type-2 t-norms on <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>N</mi><mi>C</mi></mrow></msub></math></span> composed of all normal convex fuzzy truth values: t-norms defined on the complete lattice, t_<em>r</em>-norms defined by Hernández et al., t<span><math><msub><mrow></mrow><mrow><mi>l</mi><mi>o</mi></mrow></msub></math></span>-norms defined by Harding et al., and t<span><math><msub><mrow></mrow><mrow><mi>l</mi><mi>o</mi><mi>r</mi></mrow></msub></math></span>-norms defined by Wu et al. The paper studies the relationships among these four types of type-2 t-norms constructed by generalized extended t-norms that come from the generalization of Zadeh's extension principle. Firstly, we sequentially characterize the conditions under which generalized extended t-norms satisfy each restrictive axiom in the definitions of type-2 t-norms, particularly closure properties. Then, we prove that on <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>N</mi><mi>C</mi></mrow></msub></math></span>, generalized extended t-norms being t-norms (resp. t<span><math><msub><mrow></mrow><mrow><mi>l</mi><mi>o</mi></mrow></msub></math></span>-norms) is equivalent to them being t_<em>r</em>-norms (resp. t<span><math><msub><mrow></mrow><mrow><mi>l</mi><mi>o</mi><mi>r</mi></mrow></msub></math></span>-norms). Finally, through examples, we demonstrate that on <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>N</mi><mi>C</mi></mrow></msub></math></span>, t<span><math><msub><mrow></mrow><mrow><mi>l</mi><mi>o</mi></mrow></msub></math></span>-norms (resp. t<span><math><msub><mrow></mrow><mrow><mi>l</mi><mi>o</mi><mi>r</mi></mrow></msub></math></span>-norms) are strictly stronger than t-norms (resp. t_<em>r</em>-norms) even if all of them are constructed by generalized extended t-norms.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"516 ","pages":"Article 109445"},"PeriodicalIF":3.2,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143937010","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":"QFIG: A novel attribute reduction method using conditional entropy in quantified fuzzy approximation space","authors":"Lei Yang ,&nbsp;Binbin Sang ,&nbsp;Weihua Xu ,&nbsp;Hongmei Chen ,&nbsp;Zhong Yuan ,&nbsp;Keyun Qin","doi":"10.1016/j.fss.2025.109443","DOIUrl":"10.1016/j.fss.2025.109443","url":null,"abstract":"<div><div>At present, attribute reduction based on different attribute importance measures is one of the hot topics in granular computing. Conditional entropy is a common measure to evaluate the importance of attributes in classification tasks. This paper proposes a conditional entropy based on quantified fuzzy information granular and constructs a novel attribute reduction method. First, a quantified fuzzy similarity relation is explored to overcome the instability of the existing parameterized fuzzy relations. The quantified fuzzy information granular (QFIG) induced by the defined relation and their related properties are also discussed. Second, a new QFIG-based fuzzy rough set model and its properties are proposed. Meanwhile, a general framework of the proposed fuzzy rough approximation operators is established. Third, we construct a QFIG-based conditional entropy for evaluating the importance of attributes in decision information systems. At the same time, the corresponding attribute reduction algorithm is designed based on heuristic reduction strategy. Finally, the performance of the proposed algorithm is demonstrated by numerical comparison experiments on twelve public datasets. Experimental results not only confirm the effectiveness of the proposed algorithm but also show that the performance of the proposed algorithm is better than that of some existing attribute reduction algorithms.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"516 ","pages":"Article 109443"},"PeriodicalIF":3.2,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143937008","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":"Quantale-valued maps and partial maps","authors":"Lili Shen,&nbsp;Xiaoye Tang","doi":"10.1016/j.fss.2025.109441","DOIUrl":"10.1016/j.fss.2025.109441","url":null,"abstract":"<div><div>Let <span><math><mi>Q</mi></math></span> be a commutative and unital quantale. By a <span><math><mi>Q</mi></math></span>-map we mean a left adjoint in the quantaloid of sets and <span><math><mi>Q</mi></math></span>-relations, and by a partial <span><math><mi>Q</mi></math></span>-map we refer to a Kleisli morphism with respect to the maybe monad on the category <span><math><mi>Q</mi><mtext>-</mtext><mrow><mi>Map</mi></mrow></math></span> of sets and <span><math><mi>Q</mi></math></span>-maps. It is shown that every <span><math><mi>Q</mi></math></span>-map is symmetric if and only if <span><math><mi>Q</mi></math></span> is weakly lean, and that every <span><math><mi>Q</mi></math></span>-map is exactly a map in <strong>Set</strong> if and only <span><math><mi>Q</mi></math></span> is lean. Moreover, assuming the axiom of choice, it is shown that the category of sets and partial <span><math><mi>Q</mi></math></span>-maps is monadic over <span><math><mi>Q</mi><mtext>-</mtext><mrow><mi>Map</mi></mrow></math></span>.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"516 ","pages":"Article 109441"},"PeriodicalIF":3.2,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143937009","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":"Ordinal sums of triangular norms on a bounded trellis","authors":"Jun Geng ,&nbsp;Ziwen Chen ,&nbsp;Rina Wang","doi":"10.1016/j.fss.2025.109440","DOIUrl":"10.1016/j.fss.2025.109440","url":null,"abstract":"<div><div>In this paper, we present ordinal sums of triangular norms on bounded trellises with one summand firstly by taking a right-transitive element as the left endpoint and a ∧-associative element as the right endpoint of the given interval sub-trellis. Also, the corresponding recursive construction of triangular norms on bounded trellises is shown. Meanwhile, we extend the result to the ordinal sums of triangular norms on bounded trellises with more summands including two cases that the given interval sub-trellises are contiguous or not. Particularly, we can naturally obtain two classes of triangular norms which are different from others on bounded lattices. And some illustrative examples are added for clarity.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"516 ","pages":"Article 109440"},"PeriodicalIF":3.2,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143937007","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":"Extracting business-relevance for the analysis of strategic patent portfolios from highly imprecise fuzzy estimates","authors":"Mikael Collan,&nbsp;Pasi Luukka","doi":"10.1016/j.fss.2025.109444","DOIUrl":"10.1016/j.fss.2025.109444","url":null,"abstract":"<div><div>Valuation of assets connected to forward-looking strategic investments and decision-making such as strategic patent-portfolios takes place in the presence of high uncertainty. Available information is typically in the form of vague signals and forecasts about the future and the tool that can be used to interpret it is the expert or a group of experts, because information about the structure of the future does not allow construction of models and historical data is not available. The expert estimates, from which fuzzy number estimates are constructed and aggregated, reflect the high imprecision, and extracting relevant information from them may be challenging. This paper presents how fuzzy expert estimates of strategic patent-portfolio value from multiple experts can be aggregated by using the lossless fuzzy weighted averaging without loss of relevant information and how business-relevant information can be extracted from seemingly worthlessly imprecise information, when a longitudinal set of estimates is available. A numerical case, in the context of real-world strategic patent valuation, is presented. New application of the lossless fuzzy weighted averaging and the recently introduced Luukka-Stoklasa defuzzification for general fuzzy sets is presented and results are compared with those obtained by using more traditional methods. The research offers a novel contribution to the literature on applying fuzzy logic to strategic decision-making</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"516 ","pages":"Article 109444"},"PeriodicalIF":3.2,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143942419","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}