A New Ordered Weighted Averaging Operator to Obtain the Associated Weights Based on the Principle of Least Mean Square Errors

Abstract

Determining OWA (ordered weighted averaging) weights has received more and more attention since the appearance of the OWA operator. Based on the principle of least mean squared errors, a new parametric OWA operator is proposed to obtain its associated weights. In coordination with fuzzy inference and a few of judgments on weights provided by decision makers (DMs), the new operator is carefully designed to avoid some problems of the existing ones, such as uncertainty in determining an objective function and the measure of orness, etc. Some properties of the problem are discussed to guarantee reliability in theory. A real-life problem and two simulation experiments are performed to investigate its efficiency. All results show that the proposed operator can be a useful tool to express DMs’ preference information flexibly and objectively.