Upper and lower bounds on the number of fuzzy/c switching functions

Abstract

This paper describes an estimation on the size of n-variable fuzzy switching functions with arbitrary constants ( "fuzzy/c" for short ). The whole set of fuzzy/c switching functions is divided into equivalence classes called c r -equivalent. Estimating the number of these functions in each equivalence class can be reduced to enumerating disjunctive forms of a binary switching function, which can be solved by enumerating anti-chains of the partially ordered set composed of simple phrases. Using an improved method for estimating the number of anti-chains, we can get upper and lower bounds on the number of n-variable fuzzy/c switching functions.