A general framework for ordering fuzzy sets

Authors Ulrich Bodenhofer
Editors B. Bouchon-Meunier
J. Guitérrez-Ríoz
L. Magdalena
R.R. Yager
Title A general framework for ordering fuzzy sets
Booktitle Technologies of Constructing Intelligent Systems 1: Tasks
Type in collection
Publisher Physica-Verlag
Series Studies in Fuzziness and Soft Computing
Volume 89
Mark invited
ISBN 3-7908-1454-7
Year 2002
Pages 213-224
SCCH ID# 107
Abstract

Orderings and rankings of fuzzy sets have turned out to play a fundamental role in various disciplines. Throughout the previous 25 years, a lot a different approaches to this issue have been introduced, ranging from rather simple ones to quite exotic ones. The aim of this paper is to present a new framework for comparing fuzzy sets with respect to a general class of fuzzy orderings. This approach includes several known techniques based on generalizing the crisp linear ordering of real numbers by means of the extension principle, however, in its general form, it is applicable to any fuzzy subsets of any kind of universe for which a fuzzy ordering is known—no matter whether linear or partial.