Fundamentals of fuzzy logical circuits

Fuzzy logic is characterized as an extension of two valued Boolean logic. NOT, AND and OR operators in {0,1}-valued Boolean logic are extended to [0, 1J-valued fuzzy logic. They are called fuzzy negation, t-norm and s-norm (or t-conorm), respectively. These operators can be realized in electrical circuits. A fuzzy logical circuit can be characterized as the integration of these fundamental circuits. The most important of these is the fuzzy inference circuit or fuzzy inference chip. Most inference circuits of this type are realized based on the min-max center of gravity method. This kind of fuzzy inference system is the foundation of industrial fuzzy apphcations, particularly in the field of fuzzy control. However, this technique is characterized as a fuzzy extension of combinatorial circuits in two valued Boolean logic. That is, such fuzzy inference schemas are repetitive although one stage inferences. There is therefore no need to think about memory modules or information transfer in the time axis. Ill the case of AI apphcations, e.g. fuzzy expert systems, it is necessary to introduce multi-stage fuzzy inference. In such situations, the concept of a fuzzy extension of a sequential circuit, which is a comphcation of combinatorial circuits and memory modules in two valued Boolean logic should be discussed. Thus, it is essential to introduce the notion of fuzzy memory. From this a point of view, the concept of fuzzy flip flop is presented in this paper. It is a fuzzy extension of a two valued J-K flip flop. The fundamental equations of several types of fuzzy flip flop are derived and their hardware implementations are shown. Finally, such fuzzy memory modules are combined with a fuzzy combinatorial circuit. The fundamental idea is presented in the context of the realization of fuzzy computer hardware.