Fuzzy Sets and Systems最新文献

{"title":"An efficient algorithm for estimating profust failure probability function under the assumption of probable input and fuzzy state","authors":"Xiaomin Wu,&nbsp;Zhenzhou Lu,&nbsp;Yizhou Chen,&nbsp;Kaixuan Feng","doi":"10.1016/j.fss.2024.109250","DOIUrl":"10.1016/j.fss.2024.109250","url":null,"abstract":"<div><div>Under the assumption of <strong>pro</strong>bable input and <strong>fu</strong>zzy <strong>st</strong>ate (profust), profust (also named as generalized) failure probability function (G-FPF), which varies with random input distribution parameters (DP) in the interested region, can reflect the effect of DP on structure safety and decouples the generalized reliability-based design optimization. The direct double-loop analysis of G-FPF, which repeatedly estimates the G-FPF values at different DP realizations, is time-consuming. Thus, this paper proposes a single-loop importance sampling (IS) method to estimate G-FPF by combining a variance reduction technique with a sample information-sharing strategy. The proposed method has two innovations. The first is constructing an optimal unified IS density (ISD), which is independent of the DP and envelops the interested DP region. By sharing the sample of the unified ISD, the double-loop analysis for G-FPF can be avoided, and by fusing the IS variance reduction technique, the efficiency of estimating G-FPF can be improved further. The second is designing an adaptive strategy to update the Kriging model of performance function, so that the computational cost, which is measured by the number of performance function evaluations while ensuring the acceptable precision of G-FPF estimation, can be reduced in approaching and sampling the optimal unified ISD as well as predicting the performance function at the sample of the optimal unified ISD. Moreover, the proposed method has wide applicability, and it has no restriction on the nonlinearity of the performance function and the size of the interested DP region, which is sufficiently verified by the presented examples.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"504 ","pages":"Article 109250"},"PeriodicalIF":3.2,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143159872","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":"Algebraic representations of (fuzzy) completely distributive lattices","authors":"Xiaowei Wei ,&nbsp;Yueli Yue","doi":"10.1016/j.fss.2024.109245","DOIUrl":"10.1016/j.fss.2024.109245","url":null,"abstract":"<div><div>Choosing completely distributive lattices as lattice-valued environment, this paper introduces the strong <em>L</em>-upper set monad <span><math><mi>S</mi></math></span>, studies Eilenberg-Moore algebras, Kleisli monoids and its applications of <span><math><mi>S</mi></math></span>. Concretely, we give the monad <span><math><mi>S</mi></math></span> by adjoints. Then we characterize fuzzy completely distributive lattices by its Eilenberg-Moore algebras and study Kleisli monoids of the monad. Moreover, we investigate the necessary and sufficient conditions for the establishment of <span><math><mi>S</mi></math></span>. Finally, we construct two monads, study the relationships between these two monads and <span><math><mi>S</mi></math></span>, moreover verify the rationality of the selection of lattice-valued environment by those relationships.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"503 ","pages":"Article 109245"},"PeriodicalIF":3.2,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180980","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":"P-sets","authors":"Eszter K. Horváth ,&nbsp;Leonard Kwuida ,&nbsp;Branimir Šešelja ,&nbsp;Andreja Tepavčević","doi":"10.1016/j.fss.2024.109244","DOIUrl":"10.1016/j.fss.2024.109244","url":null,"abstract":"<div><div>Starting from a poset <em>P</em> and a set <em>A</em>, we introduce <em>P</em>-sets as a natural generalization of Ω-sets. A <em>P</em>-set on <em>A</em> is defined by adding to <em>A</em> a special map from <span><math><msup><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> to <em>P</em>, which generalizes the classical equality relation. We prove that <em>P</em>-sets on <em>A</em> are naturally obtained from centralized closure systems in a family of all weak equivalences on <em>A</em>. Moreover, for every <em>P</em>-set there is a canonical representation in which the used centralized closure system replaces the poset <em>P</em>.</div><div>Further, we present a classification of all <em>P</em>-sets by the family of cuts, where <em>A</em> and <em>P</em> are fixed. Different <em>P</em>-sets may have equal collections of cut sets. Necessary and sufficient conditions under which this happens are presented; i.e., all <em>P</em>-sets are classified according to the equality of collections of cut sets.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"503 ","pages":"Article 109244"},"PeriodicalIF":3.2,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180982","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":"Breadth-first fuzzy bisimulations for fuzzy automata","authors":"Stefan Stanimirović ,&nbsp;Linh Anh Nguyen ,&nbsp;Miroslav Ćirić ,&nbsp;Marko Stanković","doi":"10.1016/j.fss.2024.109246","DOIUrl":"10.1016/j.fss.2024.109246","url":null,"abstract":"<div><div>We introduce two novel concepts: <em>fuzzy weak (bi)simulations</em> and their approximations, <em>breadth-first fuzzy (bi)simulations</em>, for fuzzy automata with membership values in an arbitrary complete residuated lattice. They offer improved approximations of the subsethood degree (equivalence degree) of fuzzy automata compared to previously established notions. Fuzzy weak (bi)simulations are defined as fuzzy relations, whereas breadth-first fuzzy (bi)simulations are characterized by decreasing sequences of fuzzy relations, where each component is a solution to a finite and linear system of fuzzy relation inequalities. Such systems consist of fuzzy sets that are nodes of the trees constructed in the classic breadth-first search manner. We provide an algorithm that computes the proposed simulations and bisimulations, along with a modified version that computes the subsethood/equality degree for given fuzzy automata. Both algorithms run in the exponential time complexity, reflecting the trade-off for achieving more precise approximations.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"503 ","pages":"Article 109246"},"PeriodicalIF":3.2,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180983","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":"H∞-optimal interval observer design for nonlinear PDE systems","authors":"Xiaona Song ,&nbsp;Zenglong Peng ,&nbsp;Zhijia Zhao ,&nbsp;Shuai Song","doi":"10.1016/j.fss.2024.109242","DOIUrl":"10.1016/j.fss.2024.109242","url":null,"abstract":"<div><div>This paper mainly focuses on the interval observer design for nonlinear partial differential equation systems with non-homogeneous Dirichlet boundary conditions. Initially, under unknown but bounded external disturbances and uncertainties caused by unmeasurable premise variables, a Takagi–Sugeno fuzzy interval observer is established to estimate the upper and lower bounds of the system state. Then, by converting non-homogeneous Dirichlet boundary conditions into homogeneous ones, the solvable conditions to ensure the stability of the upper and lower observation errors are designed. Furthermore, to improve the observation accuracy of the designed interval observer, an <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>-optimal fuzzy interval observer is designed to make the interval width more compact. Finally, the effectiveness and advantages of the designed interval observer are verified through numerical simulations.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"503 ","pages":"Article 109242"},"PeriodicalIF":3.2,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180981","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 Boolean-valued space approach to separation axioms and sobriety of bitopological spaces","authors":"Jing He,&nbsp;Dexue Zhang","doi":"10.1016/j.fss.2024.109241","DOIUrl":"10.1016/j.fss.2024.109241","url":null,"abstract":"<div><div>This paper presents a study of separation axioms and sobriety of bitopological spaces from the point of view of fuzzy topology via identifying bitopological spaces with topological spaces valued in the Boolean algebra of four elements. A system of separation axioms is proposed making use of Boolean-valued specialization order of bitopological spaces; The relationship between d-sobriety of bitopological spaces proposed by Jung and Moshier and sobriety of fuzzy topological spaces is studied; A Hofmann-Mislove theorem for bitopological spaces is established.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"503 ","pages":"Article 109241"},"PeriodicalIF":3.2,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180976","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":"Cartesian closed and stable subconstructs of [0,1]-Cat","authors":"Hongliang Lai,&nbsp;Qingzhu Luo","doi":"10.1016/j.fss.2024.109243","DOIUrl":"10.1016/j.fss.2024.109243","url":null,"abstract":"<div><div>Let &amp; be a continuous triangular norm on the unit interval <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> and <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>-<strong>Cat</strong> be the category of all real-enriched categories. Firstly, it is shown that a stable subconstruct <strong>A</strong> of <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>-<strong>Cat</strong> is cartesian closed if and only if it is determined by a suitable subset <span><math><mi>S</mi><mo>⊆</mo><msup><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> of <span><math><msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span>, where <em>M</em> is the set of all elements <em>x</em> in <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> such that <em>x</em>&amp;<em>x</em> is idempotent. Secondly, it is shown that all Yoneda complete real-enriched categories valued in the set <em>M</em> and Yoneda continuous <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>-functors also form a cartesian closed category.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"503 ","pages":"Article 109243"},"PeriodicalIF":3.2,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180978","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 n-valued Post algebras and n-valued Post logics: Twist-style representation and proof theory","authors":"Marcelo E. Coniglio ,&nbsp;Martín Figallo","doi":"10.1016/j.fss.2024.109240","DOIUrl":"10.1016/j.fss.2024.109240","url":null,"abstract":"<div><div>Mathematical Fuzzy Logic studies fuzzyness from a foundational perspective based on many-valued logics. In the early twenties of the past century, almost simultaneously, systems of many-valued logic were introduced in the respective articles of Jan Łukasiewicz and Emil L. Post, making many-valued logics a respectable field of study. Emil L. Post gave a definition of many-valued logics that was a generalization of two-valued classical logic. He defined the most important operations and discussed some of their properties by means of truth-tables. Two decades later Paul C. Rosenbloom gave a definition of an algebraic structure that served as an interpretation of Post's system; these structures are called Post algebras. Post algebras were meant to capture the algebraic properties of Post's systems. On the other hand, in his 1969 PhD dissertation, Roberto Cignoli showed that <em>n</em>-valued (<span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span>) Post algebras are Łukasiewicz-Moisil algebras containing <span><math><mi>n</mi><mo>−</mo><mn>2</mn></math></span> additional constants <span><math><msub><mrow><mi>e</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>, <span><math><mn>1</mn><mo>≤</mo><mi>i</mi><mo>≤</mo><mi>n</mi><mo>−</mo><mn>2</mn></math></span> (<span><math><msub><mrow><mi>e</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mn>0</mn></math></span> and <span><math><msub><mrow><mi>e</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>=</mo><mn>1</mn></math></span>).</div><div>In this paper, in first place, we give a representation of <em>n</em>-valued Post algebras by means of <em>generalized twist structures</em>. More precisely, we define <em>n</em>-valued twist structures as certain subsets of the product of 2<em>n</em> lattices satisfying a number of conditions; and present a suitable notion of morphism between these structures. Then, we prove that the category of <em>n</em>-valued Post algebras with its morphisms (homomorphisms in the sense of Universal Algebra) and the category of generalized twist structures with its morphisms are equivalent. On the other hand, we study some logics that arise from <em>n</em>-valued Post algebras. More precisely, we present different <em>n</em>-valued logics that naturally can be associated to <em>n</em>-valued Post algebras, namely, the non–falsity preserving logic, the truth–preserving logic, and the logic that preserves degrees of truth associated to <em>n</em>-valued Post algebras. We provide cut-free sequent calculus for the first two logics and a sequent calculus for the last one that presumably does not enjoy the cut-elimination property. Finally, it is shown that the logic that preserves degrees of truth w.r.t. <em>n</em>-valued Post algebras is a logic determined by <span><math><mi>n</mi><mo>−</mo><mn>1</mn></math></span> logic matrices.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"503 ","pages":"Article 109240"},"PeriodicalIF":3.2,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180977","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":"Archimedean property of associative aggregation operations on a bounded chain","authors":"Lingli Wang ,&nbsp;Wenwen Zong ,&nbsp;Yong Su ,&nbsp;Radko Mesiar","doi":"10.1016/j.fss.2024.109237","DOIUrl":"10.1016/j.fss.2024.109237","url":null,"abstract":"<div><div>In this paper, we focus on the Archimedean property of associative aggregation operations on a bounded chain. First, we present several equivalent characterizations of the Archimedean property. Second, we discuss the classification of associative and Archimedean aggregation operations on a bounded chain.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"502 ","pages":"Article 109237"},"PeriodicalIF":3.2,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143103486","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":"Relationships between T-transitivity indicators in (T,S,n)-fuzzy preference structures with rotation invariant t-norms","authors":"Caiping Wu ,&nbsp;Wenjing Yao ,&nbsp;Xuzhu Wang ,&nbsp;Yang Liu","doi":"10.1016/j.fss.2024.109230","DOIUrl":"10.1016/j.fss.2024.109230","url":null,"abstract":"<div><div>In this paper, based on rotation invariant <em>t</em>-norms, we investigate the <em>T</em>-transitivity indicators of various fuzzy preference relations in the setting of <span><math><mo>(</mo><mi>T</mi><mo>,</mo><mi>S</mi><mo>,</mo><mi>n</mi><mo>)</mo></math></span>-fuzzy preference structures. The investigation is twofold: (1) equivalent expressions of the <em>T</em>-transitivity indicator of the large preference and the strict preference relation, and (2) the relationships between the <em>T</em>-transitivity indicators of the large preference and those of other preference relations. As a consequence, some results on transitivity in the crisp and fuzzy preference structures are extended to their indicator versions.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"502 ","pages":"Article 109230"},"PeriodicalIF":3.2,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143103484","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}