Implication operators in fuzzy logic

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Journal Article
IEEE Transactions on Fuzzy Systems, 2002, 10 (1), pp. 88 - 91
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The choice of fuzzy implication as well as other connectives is an important problem in the theoretical development of fuzzy logic, and at the same time, it is significant for the performance of the systems in which fuzzy logic technique is employed. There are mainly two ways in fuzzy logic to define implication operators: 1) an implication operator is considered as the residuation of conjunction operator; and 2) it is directly defined in terms of negation, conjunction, and disjunction operators. The purpose of this paper is to determine the number of implication operators defined in the second way for some usual negation, conjunction and disjunction operators in fuzzy logic.
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