A probability-like new fuzzy set theory
In this paper, the reasons for the shortcoming of Zadeh's fuzzy set theory - it cannot correctly reflect different kinds of fuzzy phenomenon in the natural world - are discussed. In addition, the proof of the error of Zadeh's fuzzy set theory - it incorrectly defined the set complement that cannot exist in Zadeh's fuzzy set theory - is proposed. This error of Zadeh's fuzzy set theory causes confusion in thinking, logic and conception. It causes the seriously mistaken belief that logics of fuzzy sets necessarily go against classical and normal thinking, logic and conception. Two new fuzzy set theories, C-fuzzy set theory and probability-like fuzzy set theory, the N-fuzzy set theory, are proposed. The two are equivalent, and both overcome the error and shortcoming of Zadeh's fuzzy set theory, and they are consistent with normal, natural and classical thinking, logic and concepts. The similarities of N-fuzzy set theory with probability theory are also examined.
zadeh's fuzzy set c-fuzzy set n-fuzzy set probability classical set