Parametric Weighting Function for WOWA Operator and Its Application in Decision Making

Abstract

We propose a parametric weighting function for weighted ordered weighted averaging (WOWA) operator in decision making under uncertainty and risk environment. The weighting function is not only related to the attitude of the decision makers, but also to the event probability. Under the proposed method, the decision makers underweight small probability gains and overweight large probability gains, which is right in consistence with the psychology of the decision makers in the prospect theory. Meanwhile, it generalizes two specific weighting functions w* and w** proposed by Torra (International Journal of Intelligent Systems 12 (1997) 153–166). Moreover, the expected utility becomes a special case of the parametric weighting function for WOWA operator. To illustrate its application, an example of introducing and pricing new product is given, which shows the optimal strategies corresponding to different parameter values r.