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.
completely distributive lattices afs algebras afs structures preference relations sub-preference relations