Generating pseudo-t-norms and implication operators

Abstract

In this paper, we show that the set of all pseudo-t-norms, the set of all implications, the set of all infinitely ∨ -distributive pseudo-t-norms, and the set of all infinitely ∧ -distributive implications on a complete Brouwerian lattice are all complete lattices and lay bare the formulas for calculating the smallest pseudo-t-norm (the smallest infinitely ∨ -distributive pseudo-t-norm) that is stronger than a binary operation and the largest implication (the largest infinitely ∧ -distributive implication) that is weaker than a binary operation.