Fuzzy Rankings: Properties and Applications

Abstract: In practice, a ranking of objects with respect to given set of criteria is of considerable importance. However, due to lack of knowledge, information of time pressure, decision makers might not be able to provide a (crisp) ranking of objects from the top to the bottom. Instead, some objects might be ranked equally, or better than other objects only to some degree. In such cases, a generalization of crisp rankings to fuzzy rankings can be more useful. The aim of the article is to introduce the notion of a fuzzy ranking and to discuss its several properties, namely orderings, similarity and indecisiveness. The proposed approach can be used both for group decision making or multiple criteria decision making when uncertainty is involved.