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

Authors:
Anna Maria Radzikowska;Etienne E. Kerre
Affiliations:
Faculty of Mathematics and Information Science, Warsaw University of Technology, Warsaw, Poland;Department of Applied Mathematics and Computer Science, Ghent University, Gent, Belgium
Venue:
TARSKI'02-05 Proceedings of the 2006 international conference on Theory and Applications of Relational Structures as Knowledge Instruments - Volume 2
Year:
2006

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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 lattices 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.