Homomorphism of Latticevalued Fuzzy Finite Automata Hu Zhonggang

Homomorphism of Lattice-valued Fuzzy Finite Automata Hu Zhonggang Basic Teaching Department Nanchang Institute of Science & Technology Nanchang, Jiangxi, 330108, China E-mail: zhonggang-hu@163. com Abstract The concept of (strong) homomorphisms of lattice-valued fuzzy finite automaton is introduced, and related properties are investigated, homomorphism theorem is discussed. Eventually, the notions of admissible relation on A and kernals of strong homomorphisms are introduced, and their related properties are studied. Text System within the automation field. The system is used for studying various languages. Also, it is used to study the architecture of computing, logic operations [1 -2], as well as programming. Along with computational complexity theory and the development of science and technology, it has been widely applied in many other subjects. For example, the study of the main model of concurrent processes and the electronic computer that still be used today are the descendants of Finite automation and the Turing machine. The computational environment and calculating system are well-defined in terms of classical computing theory. However, there still remain different types of informational problems in terms of incomplete, uncertain, or inaccurate information. Similar to how there is no certain criterion to judge a person (thin or fat, rich or poor, etc. ), these issues cannot be solved by classical mathematics tools. Therefore, computing issues in an uncertain environment have become essential, and gradually have become a research topic for those who are interested in [3 -6]. Studies on computational problems in the Fuzzy Environment began with Zaden, a pioneer of Fuzzy Sets Theory. He has proposed a research topic on Fuzzy Language and Fuzzy Computing in order to develop Automata Processing Capacity, make computing intelligent, Wee [7] applies Fuzzy theory into the study of Automata, and introduces the concept of Fuzzy automato. Consequently, the study of Fuzzy Automata Theory has spread quickly and achieved a series of outstanding results [8 -14]. As humans’ uncertainty lessens, some new model fuzzy theories, such as Intuitionistic Fuzzy Theory [15], Vague theory [16], Interval Theory[17] will be used as mathematical tools to deal with issues of uncertainty and inaccuracy that have been put into the system which has enriched and developed Classical Fuzzy Theory. So far, this new Fuzzy Theory has been applied into the research of automata, such as Fuzzy Automaton[19], Vague Automaton[19] as well as Interval-valued Fuzzy Automaton[20]. Reference (21 -23) proposed fuzzy set Finite automaton is one of the researches of Fuzzy automaton. With the help of algebra, this paper has been conducted pertaining to the research on the value of homomorphism of lattice-valued fuzzy finite automata, and admissible relations and related qualities have been given out.