On Approximate Minimization of Fuzzy Automata
R. Belohlavek and M. Krupka
The paper presents a contribution to minimization of fuzzy automata. Traditionally, the problem of minimization of fuzzy automata is described as follows. Given a fuzzy automaton, describe an automaton with the minimal number of states which recognizes the same language as the given one. In this paper, we formulate a different problem. Namely, the minimal fuzzy automaton we are looking for is required to recognize a language which is similar to the language of the given fuzzy automaton to a certain degree a prescribed by a user, such as a = 0.9. That is, we relax the condition for the languages of the automata from being equal to a weaker condition of being similar to degree a. The condition of being equal is a special case for a = 1.We present answers to several problems which arise in this setting including a description of a minimal fuzzy automaton satisfying the above condition. The question of how to efficiently construct the minimal automaton is left as an open problem.
Keywords: Finite Automaton, Fuzzy Logic, Minimization.