On the distributivity of implication operations over t-representable t-norms generated from strict t-norms in interval-valued fuzzy sets theory

Abstract

Recently, many papers have appeared dealing with the distributivity of fuzzy implications over t-norms, t-conorms and uninorms. These equations have a very important role to play in efficient inferencing in approximate reasoning, especially fuzzy control systems. In [2] we have discussed the distributivity of continuous functions, in particular implication operations, over t-representable t-norms, generated from the product t-norm, in intuitionistic fuzzy sets theory. In this work we continue investigations for interval-valued fuzzy sets theory, but without any regular assumptions on an unknown function I. © Springer-Verlag Berlin Heidelberg 2010.