The EI algebra representations of fuzzy concepts

In many fuzzy systems, the membership functions of fuzzy concepts are obtained by experts' experiences. Different experts may have different membership functions for the same fuzzy concept. In this paper, the mathematical structures of fuzzy concepts are studied by the EI algebra over some axiomatic fuzzy set (AFS) structures. It is proved that any fuzzy concepts of the finite universe of discourse are the EI representations of simple concepts. By applying the AFS theory, membership functions of the fuzzy concepts can be obtained by the unitive algorithms according to the database.