A new approach to MADM problems with belief distributions based on weighted similarity measure and regret theory

Abstract

In multiple attribute decision making (MADM) problems, when belief distributions (BDs) are used to express the preference information of decision-maker, obtaining the attribute weights using the difference among the assessments is a complex but interesting challenge. This paper introduces the weighted similarity measure of belief distribution to distinguish the alternatives to the greatest extent. After proposing the concepts of similarity measure and weighted similarity measure for two belief distribution vectors, an optimization model is developed to generate the attribute weights. After that, the comparison rules and the ideal belief distributions are defined, then the regret theory is extended to rank alternatives with the consideration of the psychological behavior of the decision-maker. The main characteristic of the proposed method involves: (1) An optimization model based on weighted similarity measure is proposed to derive attribute weights in BD environment; (2) The psychological behavior is taken into account to assist the decision-maker in avoiding regret; Finally, the applicability and validity of the proposed method are demonstrated by a medical example in which doctors could make the diagnosis with minimal regret.