Semantic analysis of fuzzy models, application to Yager models

Abstract

This paper proposes a methodology to analyse the semantic behaviour of a fuzzy rule model, that is, a pair of fuzzy implication and modus ponens generating function used for inference. The proposed methodology is applied to Yager models which are obtained from Yager implication function. It is shown that, for example, Yager implicative implication is midway between the usual residual and strong implications generated from the product t-norm, and that in fact Yager implication belongs to a more general family of implications that can also be generated from the t-norms.