Interpretation of results of ranking methods with the aid of probabilistic sets

One of the fundamental issues arising in any problem in which several fuzzy sets are to be compared refers to evaluation of results obtained by means of different ranking methods. Each of them could generate a different ranking, different in the sense of numerical values of preference assigned to each fuzzy set (fuzzy alternative) and in some cases, even different in terms of the ordering obtained. Hence a suitable tool for an overall interpretation of the whole family of results is necessary. Since the family of ranking methods involves both factors of uncertainty, namely fuzziness (conveyed by the ranking results themselves) and randomness (generated by a random choice of the set of the ranking methods), we will study an approach in which probabilistic sets are put into account. It is pointed out how a subjective entropy closely associated with them can be efficiently employed for overall quantitative evaluation of the entire set of the ranking results.