Group Decision and Negotiation

, Volume 28, Issue 5, pp 907–933 | Cite as

An Analysis of Winsorized Weighted Means

  • Bonifacio LlamazaresEmail author


The Winsorized mean is a well-known robust estimator of the population mean. It can also be seen as a symmetric aggregation function (in fact, it is an ordered weighted averaging operator), which means that the information sources (for instance, criteria or experts’ opinions) have the same importance. However, in many practical applications (for instance, in many multiattribute decision making problems) it is necessary to consider that the information sources have different importance. For this reason, in this paper we propose a natural generalization of the Winsorized means so that the sources of information can be weighted differently. The new functions, which we will call Winsorized weighted means, are a specific case of the Choquet integral and they are analyzed through several indices for which we give closed-form expressions: the orness degree, k-conjunctiveness and k-disjunctiveness indices, veto and favor indices, Shapley values and interaction indices. We also provide a closed-form expression for the Möbius transform and we show how we can aggregate data so that each information source has the desired weighting and outliers have no influence in the aggregated value.


Winsorized weighted means Winsorized means Choquet integral Shapley values SUOWA operators 



The author is grateful to two anonymous referees for valuable suggestions and comments. This work is partially supported by the Spanish Ministry of Economy and Competitiveness (Project ECO2016-77900-P) and ERDF.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Departamento de Economía Aplicada, Instituto de Matemáticas (IMUVA)Universidad de ValladolidValladolidSpain

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