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.
['Van-Nam Huynh', 'Yoshiteru Nakamori', 'Tu Bao Ho', 'Germano Resconi']
A Context Model for Constructing Membership Functions of Fuzzy Concepts Based on Modal Logic