Qualitative Approximations of Fuzzy Sets and Non-classical Three-Valued Logics (I)
(0,1)-Qualitative approximations of fuzzy sets are studied by using the core and support of a fuzzy set. This setting naturally leads to three disjoint regions and an analysis based on a three-valued logic. This study combines both an algebra view and a logic view. From the algebra view, the mathematical definition of a (0,1)-approximation of fuzzy sets are given, and algebraic operations based on various t-norms and fuzzy implications are established. From the logic view, a non-classical three-valued logic is introduced. Corresponding to this new non-classical three-valued logic, the related origins of t-norms and fuzzy implications are examined.
KeywordsFuzzy set (0 and 1)-approximation non-truth functional logic three-valued logic
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