The Metric Space of Ordered Weighted Average Operators with Distance Based on Accumulated Entries

Abstract

Ordered weighted average (OWA) operators with their weighting vectors are very important in many applications. We show that directly taking Minkowski distances (including Manhattan distance and Euclidean distance) as the distances for any two OWA operator is not reasonable. In this study, we propose the standard distance measures for any two OWA operators and then propose a standard metric space for the set of all n-dimension OWA operators. We analyze and discuss some properties of the introduced OWA metric and further propose a metric space of Choquet integrals represented by the underlying fuzzy measures. Some applications in decision making of OWA distances are also presented in this study.