A General Framework for Ordering Fuzzy Sets

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.