Three Kinds of Negation of Fuzzy Knowledge and Their Base of Logic
Negative information plays an important role in fuzzy knowledge representation and reasoning. This paper distinguish between contradictory negative relation and opposite negative relation for the fuzzy information, a characteristic of fuzzy information is discovered that if a pair of opposite concepts are fuzzy concepts, then there must exists a “medium” fuzzy concept between them; conversely, if there is a medium fuzzy concept between the two opposite concepts, then opposite concepts must be fuzzy concepts. We thus consider that negation of fuzzy information include contradictory negation, opposite negation and medium negation. In order to provide a logical basis for three kinds of negation in fuzzy information, we propose a fuzzy propositional logic with contradictory negation, opposite negation and medium negation (FLcom), discussed some interesting properties of FLcom, presented a semantic interpretation of FLcom, and proved the reliability theorem.
Keywordsfuzzy knowledge fuzzy propositional logic contradictory negation opposite negation medium negation
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