Stochastic Multiple-Attribute Decision Making Method Based on Stochastic Dominance and Almost Stochastic Dominance Rules with an Application to Online Purchase Decisions

Abstract

Although some stochastic multiple-attribute decision making (SMADM) methods based on the stochastic dominance (SD) rules have been proposed, there is still the limitation that the dominance relations between some pairs of alternatives cannot be identified. In this paper, almost stochastic dominance (ASD) rules are used as supplements of the SD rules to identify dominance relations between the pairs of alternatives, and a new method for SMADM based on the SD and ASD rules is proposed. In the method, a procedure for identifying the dominance relation between each pair of alternatives based on the SD and ASD rules is given. Then, according to the identified dominance relation, the priority degree that one alternative is superior to another alternative concerning each attribute is calculated. Further, according to the obtained priority degrees, an approach for ranking alternatives is proposed using the simple weighted method. Finally, the proposed method is applied to the selection of passenger car(s) based on online ratings, and a comparison between the proposed method and the existing methods based on a numerical example is given. The proposed method can obtain more precise ranking results of alternatives. ASD rules are important supplements of the SD rules for identifying dominance relations. Based on the SD and ASD rules, the proposed SMADM method is important for developing theories and methods for SMADM.