The Seal Of The Tree Of Fuzzy Algebra And Fuzzy Language

Tree automata is a mathematical model to receive dendrolanguage, and it is thedevelopment and promotion of traditional character automata (word automata). Thetraditional tree automata is not only a basis of complexity theory, but also has beenwidely applied in many fields of learning system, pattern recognition and databasetheory. To solve the problems of continuous space or uncertain (fuzzy) informationsystems, fuzzy tree automata has been proposed. There are some research results oncongruence, homomorphism, equivalence and minimization of fuzzy tree automata.The algebra of fuzzy sets is a theoretical basis of fuzzy tree automata and its formis defined by the definition of algebra of fuzzy sets. Therefore, this thesis firstly focuseson the algebra of fuzzy sets. To explain the equivalence of different forms of fuzzydendrolanguage generating systems, building a standardized model of generatingsystems is particularly important. So this thesis studies the normal form of fuzzydendrolanguage generating systems. The closure properties of languages have beenstudied in fuzzy automata theory, namely, the closure properties of fuzzy languages.This thesis carries out research on the closure properties of fuzzy dendrolanguages. Thiswork will furtherly improve the closure properties of languages.More specifically, the main results are shown below:1. Minimum product algebra of fuzzy sets: This thesis defines the minimumproduct algebra of fuzzy sets on term algebra. We firstly prove that the property of aparticular form of n-tree meets the form of minimum product algebra of fuzzy sets byinduction hypothesis. Moreover, we prove that any linear regular equation which holdsin term algebra also holds in lattice-valued fuzzy sets, where shows the closureproperties of the equivalent class over linear regular equations. Finally, this articleproves that the algebra of fuzzy sets verifies transfinite distributive law and keepsorder-preserving.2. Normal form of F-CFDS: Based on the concepts of trees, pseudoterms, fuzzycontext-free dendrolanguage generating systems (F-CFDS) and fuzzy context-free dendrolanguages (F-CFL), this thesis proves that for any F-CFDS of order n, anequivalent F-CFDS of order n-1exists. Furthermore, for any F-CFDS, an equivalentF-CFDS of order1exists, and the thesis gives the normal form of this F-CFDS and thendescribes an example.3. Closure properties of fuzzy dendrolanguage: The relations among fuzzy treeautomata, fuzzy context-free dendrolanguage and sets of derivations trees of fuzzycontext-free grammar are discussed. This thesis defines the union, intersection,concatenation and Kleene closure operations on languages of fuzzy tree automata, givesan equivalent condition of the Kleene closure operation, and proves that the languagesof fuzzy tree automata over the four operations defined above are closed.