Universal Fuzzy Automaton

Automata theory is a. mathematics theory to study the structure, function and inter-relation of discrete mathematics system. With the development of modern technology science, the requirements of basic theory in computer science increases, as an important theory in computer science, automata theory has become the the-ory and application basis in many other subjects. As the mathematical model of computation, automaton plays an important role in many fields of computer science like text processing, compilers, hardware design and artificial intelligence applica-tion. Automaton can also act as a language recognizer for studying various forms of languages. With Zadah proposed the fuzzy set theory, the ability of linguistic recognition for automaton has been expanded to the application range of the fuzzy set theory, and then produced the fuzzy automaton. Fuzzy automaton is an expan-sion of the mathematical model of automaton, including the concept like "fuzzy""inaccurate", which makes the languages recognized by automata are closer to nature languages, and have been widely used in the field of artificial intelligence.Universal automaton is a special kind of automaton, each regular language canonically associated with a universal automaton, and every automaton recogniz-ing the language can maps to its universal automaton by a kind of morphism. This property is called universality, which is the origin of the name of universal automa-ton. Universal automaton provides a new channel for studying the minimization problem of classic finite automaton. Inspired by this, we propose the concept of universal fuzzy automaton in this paper, and discuss the properties of the univer-sal fuzzy automaton, by which can we study the minimization problem of fuzzy automaton. This forms the main topic of this paper.1. According to the properties of the fuzzy language and on the basis of the factorization of classical languages, we first define the factorizations and the left and right quotients of a fuzzy language, then discuss the algebra properties of the quotients of a fuzzy language.2. On the basis of the universal automaton, we propose the concept of universal fuzzy automaton, gives its formal models. Then we define the morphism between fuzzy automata, and discuss the relationship between fuzzy quotient automaton, fuzzy m-minimal automaton, fuzzy minimal automaton, with universal fuzzy au-tomaton. We also discuss the universality of universal fuzzy automaton and other properties of universal fuzzy automaton further. Finally, we give the presentation of the universal fuzzy automaton. We define the λ-cut of a universal fuzzy automa-ton, prove that the A-cut of the universal fuzzy automaton corresponding to a fuzzy language is just the universal automaton corresponding to the A-cut of this fuzzy language, which links universal fuzzy automaton and universal automaton together.