Pushdown Lattice-valued Automata And Fuzzy Systems

Automata are mathematical models of computations which are good at recognizing languages. Grammar are methods of describing languages which do well in generating languages. These models are used in several applied areas of computer science and provide us formal expressions of abstract problems. It is worth noting that they play a role in text processing, compilers, hard ware design and Artifical Intelligence. With the development of computer technology, the power of automata and grammar have been extended to fuzzy set theory. As a generalization of the classic automata, fuzzy automata were studied. Meanwhile, computing with words was introduced by Zadeh when the available information is too imprecise to justify the use of numbers, that is a methodology in whieh words are used in place of number for computiong and reasoning. Needless to say, words have the form of propositions expressed in natural language. So words can be applied in an important field of Artificial Intelligence-Understanding Natural Languages. Recently, professor Li proposed a new automata model based on lattice monoid- lattice-valued automata. In this paper, pushdown lattice-valued automata(PDLA) based on lattice monoid is discussed whose inputs are instead of strings of fuzzy subsets of the input alphabet. Afterwards, some propositions of context-free lattice-valued grammar(CFLG) are showed.Fuzzy logic control is one of the most active areas in fuzzy set theory, and comprises the important component of intelligent control theory. In the field of systems control, fuzzy control has been applied in solving uncertain, unlinear and time-optimal control problems, which has made great progresses in dynamic facilities, transportation, aviation and space, petroleum chemical and robot. A key aspect of fuzzy logic control is that analysising stability of fuzzy controller using unlinear functions. Then in this paper, the controllabity of fuzzy controller to controlled process is considered in the continuous condition.Concerning automata theory and fuzzy logic control, this paper is divided into two chapters:I. In automata theory, based on lattice monid, new type of computational models called PDLA and CFLG are introduced whose inputs are instead of strings of fuzzy subsets of the input alphabet. The main results are following:(1). Computing with words can be implemented by computing with values.(2). The equivalence of acceptance words by PDLA with final state and with empty stack is proved.(3). Words language generated by CFLG is closed under union and concatenation. (4). The relation between CFLG and Chomsky normal form is discussed.(5). The equivalence of words language accepted by PDLA and generated by CFLG is proved.II. In fuzzy logic control theory, the changes of system states are described by input-output relation function. In the continuous condition, the controllabity of fuzzy controller based on T-S fuzzy model to controlled process is considered. The main results are following:(1). In the continuous condition, if the original system is asymptotically stable, then the controlled system can be attained by T-S fuzzy controller in the same control performance.(2). In the continuous condition, if the original system is globel stable, then the controlled system can be attained by T-S fuzzy controller in the same control performance.