Abstract
Functional decomposition is the process of expressing a function of n variables as a composition of a number of functions, each depending on less than n variables. If the function to be decomposed is a Boolean function, then the methods proposed by Ashenhurst and Curtis can be used [2]-[6]. However, if the function is a fuzzy-valued function, then a different method is necessary to decompose the function. In this paper, after the basic definitions of fuzzy algebra are given, a brief review of the work in fuzzy switching logic is presented. The insufficiencies of Boolean methods and a previous method by Kandel [23] for the decomposition of a fuzzy switching function are discussed. A new theorem for determining if a function possesses a fuzzy simple disjunctive decomposition as well as a method for decomposing such a function are developed. Some practical applications for the decomposition of fuzzy switching functions are presented along with some open questions on this topic.
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