Orderings over Intuitionistic Fuzzy Pairs Generated by the Power Mean and the Weighted Power Mean

Abstract

In the present work, we prove a result concerning an ordering over intuitionistic fuzzy pairs generated by the power mean (Mp) for p>0. We also introduce a family of orderings over intuitionistic fuzzy pairs generated by the weighted power mean (Mpα) and prove that a similar result holds for them. The considered orderings in a natural way extend the classical partial ordering and allow the comparison of previously incomparable alternatives. In the process of proving these properties, we establish some inequalities involving logarithms which may be of interest by themselves. We also show that there exists p>0 for which a finite set of alternatives, satisfying some reasonable requirements, some of which were not comparable under the classical ordering, has all its elements comparable under the new ordering. Finally, we provide some examples for the possible use of these orderings to a set of alternatives, which are in the form of intuitionistic fuzzy pairs as well as to results from InterCriteria Analysis.