Multiple criteria decision making with interval stochastic variables: A method based on interval stochastic dominance

A novel method based on interval stochastic dominance to solve the stochastic multiple criteria decision making (SMCDM) problem with interval stochastic variables is proposed. By analyzing the uncertainty of interval stochastic variables, we propose the method of determining cumulative distribution function of interval stochastic variables. Then, three types of interval stochastic dominance (ISD) rules are investigated, the definition of interval stochastic dominance degree (ISDD) is presented and some interesting properties of ISD and ISDD are proved. With respect to the SMCDM problem with interval stochastic variables, to begin with, interval cumulative distribution functions of alternative criterion values are determined. Then, the ISD relations matrix associated with pairwise comparison of alternatives on each criterion is obtained based on ISD rules and the ISDD matrix on each criterion is calculated. Further, based on PROMETHEE-Ⅱ method, the net flows of each alternative are derived so as to obtain the ranking result. Consequently, examples are presented to illustrate the effectiveness of the proposed method.