The Generalization of Trichotomy and Its Application

Determination of the membership functions is vital in practical applications of the fuzzy sets theory. In this paper we generate the trichotomy, or in other words, we present and proof the quartering and multi-faceted. This paper is organized in the following way: in Section 2 we describe the basic theorem. Section 3 is devoted to the new theorem that we proposed. In section 4 an illustrative example is presented.