On the Least Squared Ordered Weighted Averaging (LSOWA) Operator Weights

The ordered weighted averaging (OWA) operator by Yager has received more and more attention since its appearance. One key point in the OWA operator is to determine its associated weights. Among numerous methods that have appeared in the literature, we notice the maximum entropy OWA (MEOWA) weights that are determined by taking into account two appealing measures characterizing the OWA weights. Instead of maximizing the entropy in the formulation for determining the MEOWA weights, the new method in the article tries to obtain the OWA weights which are evenly spread out around equal weights as much as possible while strictly satisfying the orness value provided in the program. This consideration leads to the least squared OWA (LSOWA) weighting method in which the program tries to obtain the weights that minimize the sum of deviations from the equal weights since entropy is maximized when the weights are equal. Above all, the LSOWA weights display symmetric allocations of weights on the basis of equal weights. The positive or negative allocations of weights from the median as a basis depend on the magnitude of orness specified. Further interval LSOWA weights are constructed when a decision-maker specifies his or her value of orness in uncertain numerical bounds.