考虑模糊集合相关性的T范式和T协范式算子

在仔细分析模糊逻辑和模糊集合论中最常用的Zadeh算子的基础上，研究了模糊集合相关性对T范式和T协范式算子运算结果的影响，并分析了Zadeh算子之所以不满足矛盾律和排中律的根本原因．最终提出了考虑集合相关性的新的T范式和T协范式算子，而且证明了该算子在不违反模糊集合的模糊性的基础上能够使模糊集合的运算满足排中律和矛盾律，并能使模糊集合理论和经典集合理论很好地统一．

New T Norms and T-Norms Operators Considering Relativity of Fuzzy Sets

In fuzzy set theory, the fuzzy set operation dissatisfy the law of contradiction and the law of excluded middle. This phenomenon is considered caused by the fuzzy property of fuzzy sets, and the viewpoint above is accepted by most researchers. But in this paper, the author analyzes the most useful operators in fuzzy logic and fuzzy set theory, and finds that classic operators like Zadeh operators have some contradiction in some problem. The author discovers that the cause of the contradiction is that the classic operators does not consider the influence the result caused by the relativity of fuzzy sets. In fact, if the fuzzy sets in the operation are correlative, the relativity of fuzzy sets should influence the result of fuzzy set operation evidently. So the author firstly defines a kind of new operators which considers the relativity of fuzzy sets. This new operators is based on Zadeh operators, and has clear definition and explicit physical meaning. The most important thing is that the fuzzy sets operation based on this operators can satisfy the law of contradiction and the law of excluded middle which can not be realized by the classic fuzzy operators, while the fuzzy property of fuzzy sets is still reserved. This work can reinforce rationality and veracity of fuzzy set theory.