Approaches to the representations and logic operations of fuzzy concepts in the framework of axiomatic fuzzy set theory I

In this paper, the representations of fuzzy concepts based on raw data have been investigated within the framework of AFS (Axiomatic Fuzzy Set) theory. First, a brief review of AFS theory is presented and a completely distributive lattice, the E#I algebra, is proposed. Secondly, two kinds of E#I algebra representations of fuzzy concepts are derived in detail. In order to represent the membership functions of fuzzy concepts in the interval [0, 1], the norm of AFS algebra is defined and studied. Finally, the relationships of various representations with their advantages and drawbacks are analyzed.