Computing With Words Formal Models And Fuzzy Automata Minimization Algorithms,

Computing with words, or CW for short is a methodology in which words are used (in place of) for computing and reasoning. Based on Lotfi A. Zadeh's work, Mingsheng Ying's work and Daowen Qiu's work, the author proposed two new formal models of computing with words, namely the formal model of computing with words via lattice-valued finite state automata and the formal model of computing with words via lattice-valued regular grammar. The formal model of computing with words is expored and investigated. As a special case of lattice-valued finite state automata, Mizumoto fuzzy finite state automaton is considred. Furthermore, we obtain a minimization algorithm of Mizumoto fuzzy automata. We obtain our results mainly by compare and contrast, analysis and synthesis, induction and reduction to absurdity. Specifical, the main results are as follows:1. Lattice-valued finite automata. We introduce the conpect of lattice-valued finite automata. The state transition function is defined as ? : Q×A×Qâ†'L, i.e.,a mapping from Q×A×Q to L, where L is a complete distributive lattice. Then we also formulate the model of computing with values via lattice-valued finite state automata, as well as the state transition function of the model of computing with words via lattice-valued finite state automata and the language accepted by lattice-valued finite automata. Lastly, we obtain a key theorem which charactarize the link between computing with words via lattice-valued finite automata and computing with numbers via lattice-valued finite automata.2. Lattice-valued regular grammar. We propose the concept of lattice-valued (hyper-) regular grammar as well as lattice-valued (hyper-) regular language. Moreover, we give the concept of the equivalence between two lattice-valued grammars. Then we proved that every lattice-valued regular language is a lattice-valued hyper-regular language. At last, we also obtain a key theorem which charactarize the link between computing with words via lattice-valued regular grammar and computing with values via lattice-valued regular grammar.3. The equivalence between two kinds of lattice-valued models. A fundamental...