Fuzzy implications and inference processes

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.