| This, essay is composed of two independent arid related parts. They are intu-itionistic fuzzy discrete event system and left-continuous interval-valued triangular norms.Since Atanassov proposed the new concept-intuitionistic fuzzy set, many schol-ars followed it and a great deal of research works have been done and the theory of intuitionistic fuzzy set developed quickly. Recall that early in 1965 the concept of fuzzy set was proposed by Zadeh which can be used to deal with lots of systems with uncertainty. The question that an object belongs to a set or not is no long defined by "Yes" or "No", but is represented by the corresponding membership function. However, membership function is a certain real number in the unit interval, while Atanassov use two real numbers instead of one single number to represent the rela-tion between an object and a given set. That is the core character of intuitionistic fuzzy set. Obviously, intuitionistic fuzzy set is more general than fuzzy set, and this is the reason why so many scholars do research on the former. Many research indi-cate that intuitionistic fuzzy set is better than fuzzy set on the aspects of practical use and hence the research on intuitionistic fuzzy set becomes more important. Of particular concern is:intuitionistic fuzzy set is a kind of interval values fuzzy set. So the interval value triangular norms which will be investigated in this essay can be used as an operator on intuitionistic fuzzy set. How to develop further discussion of this issue is a project we can research continuously.A discrete event system(DES) is a dynamic system with discrete states that are event-driven. Comparing with ordinary automaton, this system isn't required to have terminal. Therefore, it is more widely used than ordinary automaton systems. Discrete event system comes from the background rising from computer operating system to the control of complex, diverse process model. Discrete event system has been effectively used in many fields, especially in model making and control. Lin ,Ying and others opened a new setting, that is, to discuss discrete event system by using fuzzy set, and the concept of fuzzy discrete event system has been proposed. On account of the fact that intuitionistic fuzzy set is better than fuzzy set on many aspects. therefore,we combine discrete event system and intuitionistic fuzzy set theory and introduce and investigate intuitionistic fuzzy discrete system.This essay contains three chapters.In the first chapter, we introduce the preliminary knowledge which includes triangular norms, fuzzy set and intuitionistic fuzzy set, discrete event system and relevant concepts and results.The second chapter is devoted to investigate interval valued triangular norms and its left-continuity. And it also declares the relation of intuitionistic fuzzy set and interval valued fuzzy set.The third chapter introduces the concept of intuitionistic fuzzy discrete event system, builds up intuitionistic fuzzy discrete event system based on intuitionistic fuzzy automaton, discusses intuitionistic fuzzy language, studies the controllability of this language and proves necessary and sufficient conditions to it.Finally, we prove that there exists the maximal controllable sub-language of a given intuitionistic fuzzy language K, and there also exists the minimal controllable languages containing the intuitionistic fuzzy language K. |
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