A Context Model for Constructing Membership Functions of Fuzzy Concepts Based on Modal Logic

In this paper we show that the context model proposed by Gebhardt and Kruse (1993) can be semantically extended and considered as a data model for constructing membership functions of fuzzy concepts within the framework of meta-theory developed by Resconi et al. in 1990s. Within this framework, we integrate context models by using a model of modal logic, and develop a method for calculating the expressions for the membership functions of composed fuzzy concepts based on values {0, 1}, which correspond to the truth values {F, T} assigned to a given sentence as the response of a context considered as a possible world. It is of interest that fuzzy intersection and fuzzy union operators by this model are truth-functional, and, moreover, they form a well-known dual pair of Product t-norm TP and Probabilistic Sum t-conorm SP.