Approximate bisimulations for Kripke models of fuzzy multimodal logics over complete Heyting algebras

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2025-02-05 DOI:10.1016/j.fss.2025.109299

Marko Stanković , Miroslav Ćirić , Stefan Stanimirović , Đorđe Stakić

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引用次数: 0

Abstract

In this paper, we study two types of λ-approximate simulations and five types of λ-approximate bisimulations for Kripke models of fuzzy multimodal logics over complete Heyting algebras. The value λ is an element from a Heyting algebra, which serves to relax the conditions in the definitions of simulations and bisimulations. Additionally, λ represents the degree of modal equivalence between two worlds from distinct Kripke models, considering the given non-empty set of modal formulae. Further, we develop an efficient algorithm for computing the greatest λ-approximate simulation and bisimulation for every type. We also demonstrate the application of these algorithms in the state reduction of Kripke models in such a way that the reduced model preserves the same semantic properties to the extent determined by the scalar λ. We also present the algorithm that partitions the interval of the degrees of modal equivalence into subintervals with the same minimal corresponding factor fuzzy Kripke model.

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来源期刊

Fuzzy Sets and Systems 数学-计算机：理论方法

CiteScore

6.50

自引率

17.90%

发文量

321

审稿时长

6.1 months

期刊介绍： Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.