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Fuzzy implications and inference processes. (English) Zbl 1109.68119

Summary: We define fuzzy implications in general, then study their families defined from t-norms, t-conorms and strong negations. Connections between such implications and negations are established. Some basic results are presented concerning the contrapositive symmetry property. The study gives birth to a new class of t-norms. Members of this family, together with the corresponding R-implications, have attractive properties making them competitive in different applications, especially in fuzzy inference rules.

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
03B52 Fuzzy logic; logic of vagueness
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
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