Fuzzy Finite Automata Based On Computing With Words To Minimize The Problem

In this paper, we mainly introduce the theory of some different kinds of Fuzzy automata, theory of minimization of Fuzzy finite automata, the concept of Computing with words, and the problem of Computing with words via the minimization of Fuzzy finite automata. Based on professor Lan Shu's work, in which show that the characterizations of Max-Product Fuzzy Grammars and Automata, the author proposed the characterization and application of Max-Product Fuzzy Context-Free Grammars and Pushdown Automata; Then based on Lotfi A. Zadeh's work, Mingsheng Ying's work and Daowen Qiu's work, the author investigate in the minimization of a kind of Fuzzy automata with outputs and a new kind of Fuzzy automata. And the last is Computing with words via Fuzzy automata. We obtain our results mainly by compare and contrast, analysis and synthesis, induction and reduction to absurdity.Specifically, the main results are as follows:1. The investigation of Max-Product Fuzzy pushdown automata: Firstly, based on the Max-product Fuzzy finite automata, the author show the concept of Max-product Fuzzy pushdown automata and Context-free grammars; And then we obtain the equivalence of this kind of automata and the grammars; Lastly, the author show an example.2. The investigation of the minimization of a kind of Fuzzy automata with outputs: Firstly, because of the three different equivalences of two kinds of Fuzzy automata with outputs and Fuzzy finite state automata, and based on the minimization of the last kind of automata, we discuss the minimization of the first kind of automata which are more significant in abroad, and also discussed the relations between such fuzzy minimal automata and the minimal automata of fuzzy finite state automata.3. The investigation of the minimization of Computing with words via Fuzzy finite automata: Firstly, the author gave the concept of Computing with words via Fuzzy finite automata, in which we extend the Fuzzy transition function and the Fuzzy output function, such that the inputs and outputs are instead strings of fuzzy subsets of the input and output alphabet; Then, according to some equivalence relations, a minimal form is defined; Lastly, we come to the conclusion that this kind of fuzzy finite automata has an equivalent minimal fuzzy finite automata.