Product Of Intuitionistic Fuzzy Finite Automata And Its Research

Fuzzy finite state machine theory is a kind of significant mathematic model in thetheory of computation. It plays a very important role to some applications in the field ofcomputer science. The product is a basic operation in fuzzy finite state machine theory.Some imperative properties of product machines are studied and topological structuresbetween each product machine are discussed.The intuitionistic fuzzy finite state machine extends the fuzzy finite state machine.Product structures and behavior characteristics of many fuzzy finite state machines havebeen examined. Therefore, it is of great importance to investigate its algebraicproperties, product structures and behavior characteristics, especially the breakthroughof some important theories is a key to design actual systems in the computer science.The main achievements involve the following aspects:1. Based on the semigroup theory of abstract algebra and the intuitionistic fuzzy set,the intuitionistic fuzzy transformation semigroup is defined and an special intuitionisticfuzzy transformation semigroup accompanied by the intuitionistic fuzzy finite statemachine is presented. Then an intuitionistic allow relationship of the intuitionistic fuzzytransformation semigroup is introduced. The relationship between two intuitionisticfuzzy transformation semigroups is investigated on the basis of homomorphism. Finally,the paper obtains that if there exisits two homomorphic intuitionistic fuzzy finite statemachines, then two corresponding homomorphic intuitionistic fuzzy transformationsemigroups are discovered.(See Chapter3)2. The generalized direct products, cascade products and wreath products of twointuitionistic fuzzy finite state machines are principlly given. Also the definition ofcoverings is introduced. Cascade products and wreath products satisfy associativeproperty. The relationship between various products and coverings is discussed.(SeeChapter4)3. With respect to a new intuitionistic fuzzy finite state machine put forward,response function, intuitionistic accessible states, intuitionistic initial distributions,intuitionistic fuzzy tables, intuitionistic fuzzy pre-tables, behavior and intuitionistic regular are difined, considering the related some properties. Finally, four kinds ofequivalence relation and connection are given. It obtains that each intuitionistic fuzzyfinite state machine can find corresponding equivalent intuitionistic fuzzy finite statemachine with thesesholds.(See Chapter5)This paper mainly adopts constructing models and introducing parameters. Theresearch contents include intuitionistic fuzzy transformation semigroups, three kinds ofproducts of intuitionistic fuzzy finite state machines and their behaviors. Also theirtheoretical proofs are presented.