Fuzzy Implications Derived From Generalized Additive Generators of Representable Uninorms

By means of the generalized additive generators of representable uninorms, we introduce a kind of fuzzy implications, which are called $h^{-1}$ -implications. These implications are shown to be different from the known (S, N)-, R-, QL-, generalized- $h$ and $h$ -generated, and Yager’s $f$ - and $g$ -implications. Generalizations of three classical logic tautologies with implications are investigated. A series of necessary and sufficient conditions are established, under which the corresponding functional equations are satisfied.