Conversion of Fuzzy Regular Expressions to Fuzzy Automata using the Follow Automata

Abstract

Classical automata theory can not deal with uncertainty. To deal with system uncertainty, finite automata have been generalized into fuzzy automata. Stamenkovic and Ciric proposed an approach using the position automata for the construction of fuzzy automata from fuzzy regular expressions. There exist multifarious methodologies for the construction of finite automata from regular expressions known as Glushkov’s position automata, follow automata, Antimirov partial derivatives and Thompson construction etc. Antimirov’s partial derivative automata and Ilie’s follow automata are the quotient of the Glushkov’s position automata. For the construction of fuzzy automata from regular expressions, if position automata is used then numbers of states are always n + 1 (where n is total count of input alphabets that are presented in the regular expression) and whereas if follow automata is used then numbers of states are equal to or less than n + 1 (where n is total count of input alphabets that are presented in the regular expression). In this thesis, an approach for the conversion of fuzzy regular expressions to fuzzy automata using the concept of follow automata has been proposed. The number of states of the obtained Fuzzy automata using the proposed approach is lesser than the extant approaches in the literature without increasing the complexity. Using theorem, it has been proved that the language accepted by the fuzzy regular expression and fuzzy automata are same.