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Intuitionistic fuzzy implication operators – an expression and main properties. (English) Zbl 1054.03022

The paper discusses two different objectives. From the introduction: “The first is to define and study the concept of implication operator when the propositions \(p\), \(q\) of the conditional “if \(p\) then \(q\)” are intuitionistic fuzzy. That is, when each one of them is defined by two values, where the first indicates the degree of truth of the proposition and the second the degree of non-truth. … The second objective is to present a general expression of the intuitionistic fuzzy implication operators in function of fuzzy implications acting on aggregations of the possible values of truth and aggregations of the possible values of non-truth. We then analyze the conditions the selected aggregation operators and the fuzzy implications used must satisfy in order for our implications to satisfy different properties.”

MSC:

03B52 Fuzzy logic; logic of vagueness
68T27 Logic in artificial intelligence
68T37 Reasoning under uncertainty in the context of artificial intelligence
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