Switching and Finite Automata Theory: Computer Science Series
Switching and Finite Automata Theory: Computer Science Series
Fuzzy Switching and Automata: Theory and Applications
Fuzzy Switching and Automata: Theory and Applications
A chart method for simplifying truth functions
ACM '52 Proceedings of the 1952 ACM national meeting (Pittsburgh)
Complex Disjunctive Decomposition of Incompletely Specified Boolean Functions
IEEE Transactions on Computers
Minimization of Fuzzy Functions
IEEE Transactions on Computers
Fuzzy Logic and its Application to Switching Systems
IEEE Transactions on Computers
IEEE Transactions on Computers
On the Decomposition of Fuzzy Functions
IEEE Transactions on Computers
On Minimization of Fuzzy Functions
IEEE Transactions on Computers
Journal of Computer and System Sciences
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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.