The representations of fuzzy concepts based on the fuzzy matrix theory and the AFS theory

In many fuzzy systems, the membership functions of fuzzy concepts are obtained by the expert's experiences. Different persons may have different membership functions for the same fuzzy concept and the current algorithms for determining membership functions are not universal. So that many mathematical tools can not applied to the fuzzy model. In this paper, the mathematical structures of fuzzy concepts have been studied by the EI algebra which is molecular lattice defined by Wang Guojun over some AFS (Axiomatic Fuzzy Set) structures which is super-graph and the fuzzy matrix theory. It is proved that any fuzzy concepts of the finite universe of discourse are the EI representations of simple concepts, which can be represented by the sub-perfect relation defined by Kim K.H.. Applying the AFS theory and the fuzzy matrix theory, the membership functions of the fuzzy concepts can be obtained by the unitive algorithms according to the database. And many powerful mathematical tools such as lattice theory, topological molecular, combinatorics etc. can be applied to study fuzzy model.