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

Abstract

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.