Fuzzy information relations and operators: An algebraic approach based on residuated lattices

Abstract

We discuss fuzzy generalisations of information relations taking two classes of residuated lattices as basic algebraic structures. More precisely, we consider commutative and integral residuated lattices and extended residuated l attices defined by enriching the signature of residuated lattices by an antitone involution corresponding to the De Morgan negation. We show that some inadequacies in representation occur when residuated lattices are taken as a basis. These inadequacies, in turn, are avoided when an extended residuated lattice constitutes the basic structure. We also define several fuzzy information operators and show characterizations of some binary fuzzy relations using these operators. © Springer-Verlag Berlin Heidelberg 2006.