2017/10/24 by Chao Yang, Yongming Li · 1 citation
Computer Science · #Advanced Algebra and Logic #Formal Methods in Verification #semigroups and automata theory
paper · doi:10.1109/tfuzz.2017.2760278
openalex publication_date 2017/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/26
This paper investigates the approximate bisimulation relations for fuzzy automata in order to study the approximate minimization problem of fuzzy automata. For a small positive real number ∈, we introduce the notion of ∈-bisimulation relations between two fuzzy automata, and prove that the behavior of a fuzzy automaton A differs by ∈ from the behavior of a fuzzy automaton B under a ∈-bisimulation relation between them. Also, the notion of surjective functional ∈-bisimulation relations between two fuzzy automata is defined. According to surjective functional ∈-bisimulation relations, we discuss ∈-bisimulation relations for a fuzzy automaton. A construction of aggregated fuzzy automaton by the given ∈-bisimulation for a fuzzy automaton is given. Furthermore, we find that there might not exist the greatest ∈-bisimulation relation for a fuzzy automaton, and we novelly give an effective algorithm to construct all maximal ∈-bisimulation relations for the given fuzzy automaton. Finally, we point out that bisimulation relations for a fuzzy automaton are also ∈-bisimulation relations, the conditions for the real number ∈ to ensure the existence of the greatest ∈-bisimulation are also discussed.