Fuzzy Finite Automata Minimization Algorithms

In this paper, based on fuzzy finite automata(FA), the new algorithm of minimal fuzzy automata and fuzzy attributive automata are concerned.In Chapter 1, the conceptions of fuzzy set and fuzzy automata are given.In Chapter 2, we present a new semi-incremental algorithm, which combined with properties of acyclic deterministic fuzzy automata. Because the algorithm is related with fuzzy membership, we would present some novel functions which make the new algorithm different to general algorithm and moreover it can be used in the condition which there are multi-incoming (transitions) states by applying build-imitate state. So the new semi-incremental algorithm is more useful and practiced.In Chapter 3, we establish some concepts in fuzzy generalized automata (FGA). We then present a new algorithm, which would calculate the minimal fuzzy generalized automata (FGA). The new algorithm is composed of two parts: the first is called E-reduction, which contracts states that are equivalent and the second is called RE- reduction, which removes states which are in the maximal acyclic subgraph.In Chapter 4, we not only give a new definition of fuzzy finite automata, of which the state transition accords with a compound fuzzy transition, but also present an important conclusion that the coarsest respecting compound fuzzy transition partition of states is same with the coarsest equivalent partition. In the discussion of coarsest partition, we give an algorithm respecting compound fuzzy transition which would be applied to get the coarsest respecting compound fuzzy transition partition. Of course, the algorithm gives the running time and terminating condition. So it is more useful and easy to implement.In Chapter 5, the concepts of fuzzy attributive regular grammar and fuzzyattributive automata are introduced. In recognizing process, the fuzzy attributive automata can depict the difference between known sentences and unrecognized sentences. Therefore, it has wide application.