R-FUZZY SETS

The theory of fuzzy sets was founded by Zadeh as an approach to cope w ith the pressing need to deal with phenomena which cannot be modelled properly by conventional mathematics because they contain factors whic h are fuzzy in nature. However, in this frame of the theory of fuzzy s ets, we cannot discern two conflicting fuzzy conceptions properly, and therefore, the excluded middle law is violated. In this theory, one d oes not differ fuzzy sets from their membership functions. That is, a fuzzy set in the sense of Zadeh is equivalent to its membership functi on. This may be the main reason why the excluded middle law was violat ed. In this paper, we try to provide a mathematical frame of fuzzy set s theory, such that it can not only eliminate the suspicion for the ob jective reality of membership functions of fuzzy sets, but also avoid violating the excluded middle law. In our frame, fuzzy sets and their membership functions are not equivalent conceptions.