Article ID Journal Published Year Pages File Type
6857648 Information Sciences 2015 17 Pages PDF
Abstract
In this paper, we first discuss some properties of residuum and deresiduum of a binary operation on a complete lattice. Then, we investigate the relations between residuum and deresiduum. Finally, we demonstrate how each individual logical character of a right infinitely ∧-distributive implication, such as the law of importation, the weak exchangeability principle, the exchange principle, the contrapositive symmetry and the contraction law, can be translated into a property of its deresiduum. Moreover, we give some conditions under which deresiduum of a right infinitely ∧-distributive implication is, respectively, a left (right) uninorm, pseudo-uninorm and uninorm, and show that right infinitely ∧-distributive implications, which satisfy the weak exchangeability principle and the contrapositive symmetry, can be presented by commutative conjunctors and strong negations.
Related Topics
Physical Sciences and Engineering Computer Science Artificial Intelligence
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