Pseudo-t-norms and implication operators on a complete Brouwerian lattice
In this paper, we introduce and discuss the concept of pseudo-t-norms on a complete Brouwerian lattice L, study the relation between the set of all infinitely boolean OR-distributive pseudo-t-norms and the set of all infinitely boolean AND-distributive implications on L in detail, and point out that three classes fundamental fuzzy implications and Yager's implication on [0, 1] are all infinitely boolean AND-distributive implications that can be induced by infinitely boolean OR-distributive pseudo-t-norms on L when L = [0, 1]. We also give out a method for generating pseudo-t-norms and implications on L. (C) 2002 Elsevier Science B.V. All rights reserved.
pseudo-t-norm implication non-classical logic t-norm weak t-norm strong negation