The monoid structure of e-implications and pseudo-e-implications

In this paper we consider the set of all e-implications and pseudo-e-implications. We define operators to endow these sets as monoid structures which are also complete lattices. The set of all pseudo-e-implications becomes a De Morgan algebra. We introduce a class of e-implications such that it becomes a De Morgan algebra. Moreover contrapositive and self-dual pseudo-e-implication and contrapositive e-implication are also studied. Finally we introduce a class of pseudo-e-implications such that it becomes a complete sublattice of the set of all pseudo-e-implications, which is also a De Morgan algebra.