Algebraic properties of approximate bisimulation relations for fuzzy automata

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS Fuzzy Sets and Systems Pub Date : 2025-01-16 DOI:10.1016/j.fss.2025.109278

Ping Li , Jufang Yang , Yongming Li , Chao Yang , Wenyu Xue

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引用次数: 0

Abstract

The paper introduces ε-bisimulation relation, surjective

L

-functional ε-bisimulation relation, surjective functional ε-bisimulation relation, bijective functional ε-bisimulation relation and ε-isomorphism from fuzzy automata

A

B

by fuzzy matrices. Then it is proved that the behavior of a fuzzy automaton

A

differs from the behavior of a fuzzy automaton

B

by at most ε if there exists a ε-bisimulation relation between them. In particular, if there exists a surjective

L

-functional ε-bisimulation relation between them, we give a more concise proof of above conclusion by fuzzy matrices. Moreover, the notion of ε-bisimulation equivalence relation on a fuzzy automaton is given by fuzzy matrices. Based on two different constructions of quotient fuzzy automata, the relationships between ε-bisimulation relations and ε-bisimulation equivalence relations and the ε-Isomorphism theorems of quotient fuzzy automata are given.

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本文介绍了ε-二拟合关系、投射 L 函数ε-二拟合关系、投射函数ε-二拟合关系、双投射函数ε-二拟合关系以及模糊矩阵从模糊自动机 A 到 B 的ε-同构。然后证明，如果模糊自动机 A 与模糊自动机 B 之间存在ε-二拟合关系，则它们的行为最多相差 ε。特别是，如果它们之间存在一个投射 L 函数ε-双拟合关系，我们将通过模糊矩阵对上述结论给出更简洁的证明。此外，模糊矩阵给出了模糊自动机上的ε-双模拟等价关系概念。基于商模糊自动机的两种不同构造，给出了ε-双拟合关系和ε-双拟合等价关系之间的关系以及商模糊自动机的ε-同构定理。

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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.