On the Properties of Fuzzy Switching Functions

Abstract

A strictly binary approach to the treatment of switching circuits today is not always adequate to describe systems in the real world. This approach is partly due, to the relative simplicity of designing binary switching systems, and to the fact that basic switching modules in common use are two-positional. Consequently, every variable in Boolean logic is assumed to be two-valued. However, because of real-world constraints, the attributes of system variables are often ambiguously defined. In other words, quite often variables might have values other than falsehood and truth. Cases with such attributes arise, for example in artifical intelligence and related subjects. Ever since Zadeh introduced the idea of fuzzy set theory 11 by utilizing the concept of membership grade, a number of authors have been concerned with the analysis and applications of fuzzy models. Especially, the relation of fuzzy to switching systems have been discussed in 2]–12] and by other researchers in relation to other topics.

In this paper we are concerned with the study of fuzzy switching functions and their properties. Special attention is devoted to their minimization, enumeration, and their application to Boolean static hazard detection.