On a New Class of Implications: (G, Min)-Implications and Several Classical Tautologies

A new class of fuzzy implications, called (g,min)-implications, is introduced by means of the additive generators of continuous Archimedean t-conorms, called g-generators. Basic properties of these implications are discussed. It is shown that the (g,min)-implications are really a new class different from the known (S,N)-, R-, QL- and Yager's f- and g-implications. Generalizations of three classical logic tautologies with implications, viz. law of importation, contraction law and distributivity over triangular norms (t-norms) and triangular conorms (t-conorms) are investigated. A series of necessary and sufficient conditions are proposed, under which the corresponding functional equations are satisfied.

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