Level cut conditioning approach to the necessity measure specification

Abstract

A necessity measure N is defined by an implication function. However, specification of an implication function is difficult. Necessity measures are closely related to inclusion relations. In this paper, we propose an approach to necessity measure specification by giving an equivalent parametric inclusion relation between fuzzy sets A and B to NA(B) ≥ h. It is shown that, by such a way, we can specify a necessity measure, i.e., an implication function. Moreover, given an implication function, an associated inclusion relation is discussed.