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.