Some remarks on the LSOWA approach for obtaining OWA operator weights

Abstract

One of the key issues in the theory of ordered-weighted averaging (OWA) operators is the determination of their associated weights. To this end, numerous weighting methods have appeared in the literature, with their main difference occurring in the objective function used to determine the weights. A minimax disparity approach for obtaining OWA operator weights is one particular case, which involves the formulation and solution of a linear programming model subject to a given value of orness and the adjacent weight constraints. It is clearly easier for obtaining the OWA operator weights than from previously reported OWA weighting methods. However, this approach still requires solving linear programs by a conventional linear program package. Here, we revisit the least-squared OWA method, which intends to produce spread-out weights as much as possible while strictly satisfying a predefined value of orness, and we show that it is an equivalent of the minimax disparity approach. The proposed solution takes a closed form and thus can be easily used for simple calculations. © 2009 Wiley Periodicals, Inc.

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