On minimal realization for a fuzzy language and Brzozowski’s algorithm

Article type: Research Article

Authors: Tiwari, SP^{a; *} | Gautam, Vinay^a | Davvaz, Bijan^b

Affiliations: [a] Department of Applied Mathematics, Indian School of Mines, Dhanbad, India | [b] Department of Mathematics, Yazd University, Yazd, Iran

Correspondence: [*] Corresponding author. S.P. Tiwari, Department of Applied Mathematics, Indian School of Mines, Dhanbad 826004, India. Tel.: +91 326 2235480; Fax: +91 326 2235580; E-mail: sptiwarimaths@gmail.com.

Abstract: The purpose of the present work is to provide a simpler solution of a well-known characterization of fuzzy regular languages and a minimal realization for given fuzzy language by using Brzozowski’s algorithm. In between, we associate two crisp deterministic fuzzy automata with a given crisp deterministic fuzzy automaton and show that the reachability and observability maps of the given crisp deterministic fuzzy automaton turn out to be morphisms of category of all crisp deterministic fuzzy automata.

Keywords: Crisp deterministic fuzzy automaton, reachability map, observability map, fuzzy language, minimal realization

DOI: 10.3233/IFS-151673

Journal: Journal of Intelligent & Fuzzy Systems, vol. 29, no. 5, pp. 1949-1956, 2015