A Extended TOPSIS Method for the Stochastic Multi-Criteria Decision Making Problem through Interval Estimation

In this paper, a new method is presented for stochastic multi-criteria decision making (SMCDM) problem with incomplete weight information based on the traditional idea of TOPSIS method. In this approach, the SMCDM problem can be converted into an interval multi-criteria decision making (IMCDM) problem by interval estimation. In order to avoid the rank reversal phenomenon, the modified TOPSIS method is proposed by the concept of absolute positive and negative ideal solutions. Meanwhile, the interval values of relative closeness are computed using the simple nonlinear programming. The average relative closeness is obtained to determine the ranking of alternatives. Finally a numerical example is given to illustrate the effectiveness and practicality of proposed method.