Breadth-first fuzzy bisimulations for fuzzy automata

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS Fuzzy Sets and Systems Pub Date : 2024-12-17 DOI:10.1016/j.fss.2024.109246

Stefan Stanimirović , Linh Anh Nguyen , Miroslav Ćirić , Marko Stanković

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Abstract

We introduce two novel concepts: fuzzy weak (bi)simulations and their approximations, breadth-first fuzzy (bi)simulations, 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.

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我们提出了两个新概念：模糊弱（bi）模拟及其近似值--广度优先模糊（bi）模拟，适用于在任意完整残差网格中具有成员值的模糊自动机。与以前建立的概念相比，它们提供了更好的模糊自动机子实体度（等价度）近似值。模糊弱（双）模拟被定义为模糊关系，而广度优先模糊（双）模拟的特征是模糊关系的递减序列，其中每个组成部分都是模糊关系不等式的有限线性系统的解。这种系统由模糊集合组成，这些模糊集合是以经典的广度优先搜索方式构建的树的节点。我们提供了一种算法，可以计算建议的模拟和二模拟，以及一种修改版算法，可以计算给定模糊自动机的子实体/不等度。这两种算法的运行时间复杂度都是指数级的，反映了为获得更精确的近似值所做的权衡。

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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.