Overlap Indices: Construction of and Application to Interpolative Fuzzy Systems

Abstract

In this paper, we analyze the minimal set of axioms that overlap indices between fuzzy sets must fulfill. We also present a method to build overlap indices using overlap functions, and we carry on a theoretical study about the continuity, the invariance, and some general properties of such indices. We present a generalization of the inference algorithm for interpolative fuzzy systems using overlap indices. We also propose an algorithm for choosing, among a set of overlap indices, the best one for a considered problem.