Two types of implications derived from uninorms

This work deals with two kinds of operators derived from uninorms. On the one hand, QL-operators defined by IQ(x,y)=U′(N(x),U(x,y)) for all x,y∈[0,1], where N is a strong negation and U and U′ are a conjunctive and a disjunctive uninorm, respectively. On the other hand, the contraposition of QL-operators, called D-operators given by ID(x,y)=U′(U(N(x),N(y)),y). In both cases, a necessary condition on U′ is given in order for IQ and ID to be implication functions, and in a particular continuous case, necessary and sufficient conditions are given. Finally, several properties are studied and the non-continuous case is also discussed.