Fuzzy implications defined on the set of discrete fuzzy numbers

Abstract

Given an implication function I defined on the finite chain L = {0,...,n}, a method for extending I to the set of discrete fuzzy numbers whose support is a set of consecutive natural numbers contained in L (denoted by A L ) is given. The resulting extension is in fact a fuzzy implication on A L preserving some boundary properties. Moreover, if the initial implication I is an S, QL or D-implication on L then its extension is also an S, QL or D-implication on A L , respectively.