关键词: 模糊逻辑, 矛盾否定, 对立否定, 中介否定, 中介模糊公式

Abstract: For different kinds of negative relations in fuzzy knowledge, Pan Zhenghua pointed out that the negations in fuzzy knowledge should be composed of three distinct classes: contradictory negation, opposite negation and medium negation, and proposed the fuzzy sets with contradictory negation, opposite negation and medium negation denoted as FScom. Subsequently, the author presented a kind of improved fuzzy set IFScom (improved fuzzy sets with contradictory negation, opposite negation and medium negation). Firstly, this paper proposes a novel type of fuzzy propositional logic which corresponds to FScom and IFScom. Then, it gives the infinite-valued semantic model and satisfiability of FPcom, and proves the soundness theorem and the completeness theorem of FPcom. In some sense, FPcom may be considered as an improved medium propositional calculus system.

Key words: fuzzy logic, contradictory negation, opposite negation, medium negation, medium fuzzy formula