Study On Fuzzy Regular Language And Fuzzy ω Regular Language

In this paper, algebraic sfructures and properties offuzzy regular language are discussed based on the achievements of such scholars as J N Mordeson[9,11?13], E S Santos[16.-20], Zhiwen Mo, Lan Shu[5,6,21], Jizhong Shen[7,1O], Jiayin Peng[46,47]. These scholars have studied fuzzy finite-stale automaton with outputs, fuzzy regular language studied by these scholars is pertinent to pure fuzzy formal language theory as well as fuzzy automaton with the employment of fuzzy mathematics. The paper is grounded on fuzzy finite state automaton and language established by E T Lee and L A Zadeh in 1969. The representation of fuzzy regular language is chiefly class j/ied into three types as following: (1) Fuzzy finite-state automaton (deterministic and non-deterministic); (2) Fuzzy regular expression;(3)Fuzzy linear grammar(right linear grammar and left linear grammar). In the paper, three basic theorems offi zzy regular Ian guage leene theorems, Pumping lemma and MyhilI-Nerode's theorem---are developed in terms offuzzy form through fuzzy finite automaton without outputs. The three theorems lay a foundation of studying fuzzy regular language further, and reflect the relationship between fuzzy regular language and fuzzy finite state automaton. Based on these researches, the equivalent of two types offuzzy finite automaton is achieved, on which are combined properties of two fuzzy finite automaton which develop parallel. Because fuzzy linear grammar is regarded as one representation offuzzy regular language, we discuss properties of fuzzy regular language and the relationships among fuzzy rational language, fuzzy right linear grammar, fuzzy left linear grammar and fuzzy regular language in section four and five of Chapter One in the perspective of formal grammar. The formal deduction is of great help to realize theoretical results offuzzy regular language. In Chapter Two, finite power property and Abelian properties offuzzy regular language are discussed, and some sigmficant conclusions are drawn, which offers an useful solution to the perplexing and interesting problem. For the sake of enriching fuzzy formal language, the preliminary study of fuzzy regular language and fuzzy context-free language is made on the basis of the discussion of the previous chapters.