This paper discusses recent applications of fuzzy sets and the theory of approximate reasoning. The primary focus is on fuzzy logic control (FLC). We begin with a brief history of the key ideas, a survey of recent applications, and a discussion of the genesis of FLC in Japan. We then turn to a study of the general principles of FLC, considering it as a combination of ideas from conventional control theory, artificial intelligence, andfuzzy sets theory. We next provide a detailed analysis of a simple application in consumer electronics, namely, a fuzzy washing machine developed by Hitachi Corporation. In concluding sections we briefly consider other types of applications, including recent work on pilotless helicopters, fuzzy expert systems, and the concept of afuzzy computer, and we discuss the potential for future developments. It is our opinion that the subject of FLC is still very much in its infancy, and that recent events mark the beginning of an entirely new genre of "intelligent" control.

Fuzzy automata have long been accepted as a generalization of nondeterministic finite automata. A closer examination, however, shows that the fundamental property-nondeterminism-in nondeterministic finite automata has not been well embodied in the generalization. In this paper, we introduce nondeterministic fuzzy automata with or without -moves and fuzzy languages recognized by them. Furthermore, we prove that (deterministic) fuzzy automata, nondeterministic fuzzy automata, and nondeterministic fuzzy automata with -moves are all equivalent in the sense that they recognize the same class of fuzzy languages.

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