Sensitivity analysis of the ordered weighted averaging operator via linear models

Abstract

The efficient computation of the weights in an ordered weighted averaging (OWA) operator plays an important role in the successful design and application of the OWA operator. In some applications, an OWA weight vector with positive and distinct components for any desired orness level is preferable. This paper proposes two complementary linear OWA (CLOWA) models for determining the weights and a compact form of the optimal weights in the general case (i.e., for any level of orness and n). The proposed models produce a unique OWA weight vector with distinct and positive components for any orness level α∈(0,1). In addition to a combined goodness measure, the sensitivity analysis on the outputs of theOWA operator with respect to the optimism degree of the decision maker (DM) is important. This study obtains the combined goodness measure and sensitivity analysis models for two linear methods: the minimax disparity (MD) and new proposed models. Then, to assign reliable ranks to the alternatives in the presence of two conflicting objectives—maximizing the combined goodness measure and minimizing its sensitivity to the optimism degree of the DM—the composite measure of goodness is extended. The proposed methods are applied in a water resource management problem.