Symmetric weights for OWA operators prioritizing intermediate values. The EVR-OWA operator

Abstract

One of the most widely adopted approaches to define weights for Ordered Weighting Averaging (OWA) operators consists of using biparametric linear increasing fuzzy linguistic quantifiers. However, several shortcomings appear when using these quantifiers because depending on the values of these parameters, the aggregations could be biased or the extreme values might be completely ignored. In this contribution, the use of Extreme Values Reductions (EVRs) as fuzzy linguistic quantifiers is proposed to define weights for OWA operators in order to provide more realistic aggregations. First, the impact of the parameters of these linear fuzzy linguistic quantifiers in the OWA aggregations is studied. After that, EVR-OWA operators are introduced as those OWA operators whose weights are computed by using an EVR as fuzzy linguistic quantifier. It will be shown that when using EVR-OWA operators to fuse information, the aggregations are non-biased, take into account more information and the intermediate values are prioritized before the extreme ones. After proposing several families of EVRs, the generalising potential of the EVR-OWA operators is shown by proving that every family of symmetric weights for OWA operators that prioritize the intermediate information are the weights obtained from a certain EVR. Finally, an illustrative example is provided.