Orness Measure of OWA Operators: A New Approach

Abstract

The ordered weighted averaging (OWA) operators are an extensively used class of aggregation operators. The weight vector that is associated with an OWA can determine the attitudinal characters of the aggregation. One of these characterizing measures is called the orness measure. The aim of this paper is to introduce orness measures in an axiomatic framework and to propose an alternate definition of orness that is based on these axioms. The proposed orness measure satisfies a more generalized set of axioms than Yager's orness measure. We further calculate the maximum Shannon's entropy of the OWA operator corresponding to a fixed value of orness of our proposed measure as well as of Yager's orness. For a given level of orness, the maximum entropy corresponding to the proposed orness measure, is more than that of Yager's. This suggests that the proposed measure is a more plausible one.