Type 2 t-Norms and Extended t-Norms

Abstract

This research work treats multiplicative conjunctive operations in type 2 fuzzy logic. In the previous work, the authors gave the axiomatic definition of type 2 t-norms, and proposed a method to construct them from the conventional (i.e. type 1) t-norms via the extension principle, which were named extended t-norms. In the present report, the authors investigate in detail the inclusion relation between the set of type 2 t-norms and that of extended t-norms, and also give the necessary and sufficient condition for type 2 t-norms so that they could be expressed as the extended t-norms.