Some Results of Fuzzy Turing Machines

In this paper we study the variants of fuzzy Turing machines and universal fuzzy Turing machine. First we give several equivalent formulations of fuzzy Turing machines which correspond to fuzzy deterministic Turing machines (FDTMs), fuzzy nondeterministic Turing machines (FNTMs) and multitape fuzzy Turing machines. Then the notions of fuzzy recursively enumerable languages and fuzzy recursive languages are defined in terms of FDTMs. The level characterizations of fuzzy recursively enumerable languages and fuzzy recursive languages are exploited. Second, we show that there is no universal fuzzy Turing machine that can simulate any fuzzy Turing machine on it. Finally, we propose the notion of complexity classes of fuzzy languages by using the time-bounded fuzzy Turing machines. In particular, the notions of fuzzy polynomial time-bounded computation (FP) and fuzzy nondeterministic polynomial time-bounded computation (FNP) are introduced, their connections to P and NP are also characterized