Affiliations: Department of Electronics and Information Systems, Graduate School of Engineering, Osaka University, 2-1, Yamada-oka, Suita, Osaka 565-0871, JAPAN. E-mail: inuiguti@eie.eng.osaka-u.ac.jp | Department of Electronics and Information Systems, Graduate School of Engineering, Osaka University, 2-1, Yamada-oka, Suita, Osaka 565-0871, JAPAN. E-mail: tanino@eie.eng.osaka-u.ac.jp
Note: [] Address for correspondence: Department of Electronics and Information Systems, Graduate School of Engineering, Osaka University, 2-1, Yamada-oka, Suita, Osaka 565-0871, JAPAN
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 a parametric inclusion relation between fuzzy sets A and B which is equivalent to NA(B) ≥ h. It is shown that, in such a way, we can specify a necessity measure, i.e., an implication function. Moreover, when a necessity measure or equivalently, an implication function is given, then the derivation of an associated parametric inclusion relation is discussed. The associated parametric inclusion relation cannot be obtained for any implication function but only for implication functions which satisfy certain conditions. Applying our results to necessity measures defined by S-, R- and reciprocal R-implications with continuous Archimedean t-norms, associated parametric inclusion relations are shown.
