A similarity-based generalization of fuzzy orderings preserving the classical axioms
|Titel||A similarity-based generalization of fuzzy orderings preserving the classical axioms|
|Journal||International Journal of Uncertainty, Fuzziness Knowledge-Based Systems|
Equivalence relations and orderings are key concepts of mathematics. For both types of relations, formulations within the framework of fuzzy relations have been proposed already in the early days of fuzzy set theory. While similarity (indistinguishability) relations have turned out to be very useful tools, e.g. for the interpretation of fuzzy partitions and fuzzy controllers, the utilization of fuzzy orderings is still lagging for behind, although there are a lot of possible applications, for instance, in fuzzy preference modeling and fuzzy control. The present paper is devoted to this missing link. After a brief motivation, we will critically analyze the existing approach to fuzzy orderings. In the main part, an alternative approach to fuzzy orderings, which also takes the strong connection to gradual similarity into account, is proposed and studies in detail, including several constructions and representation results.