A new class of fuzzy implications derived from generalized h-generators

A new class of fuzzy implications, called ( h , min ) -implications, is introduced by means of generalized h-generators. Basic properties of these implications are discussed. It is shown that the ( h , min ) -implications are really a new class different from the known (S,N)-, R-, QL- and Yagerʹs 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 established, under which the corresponding functional equations are satisfied.