Distance measures, weighted averages, OWA operators and Bonferroni means

[EN] The ordered weighted average (OWA) is an aggregation operator that provides a parameterized family of operators between the minimum and the maximum. This paper presents the OWA weighted average distance operator. The main advantage of this new approach is that it unifies the weighted Hamming distance and the OWA distance in the same formulation and considering the degree of importance that each concept has in the analysis. This operator includes a wide range of particular cases from the minimum to the maximum distance. Some further generalizations are also developed with generalized and quasi-arithmetic means. The use of Bonferroni means under this framework is also studied. The paper ends with an application of the new approach in a group decision making problem with Dempster-Shafer belief structure regarding the selection of strategies.
We would like to thank the editor-in-chief, the associate editor and the anonymous reviewers for valuable comments that have improved the quality of the paper. Support from the project PIEF-GA-2011-300062 from the European Commission and from the University of Chile is gratefully acknowledged