A method for stochastic multiple attribute decision making based on concepts of ideal and anti-ideal points

This paper proposes a novel method for solving the stochastic multiple attribute decision making (SMADM) problem, where consequences of alternatives with respect to attributes are represented by random variables with cumulative distribution functions. First, the concepts of ideal and anti-ideal cumulative distribution functions are introduced, and the related theoretical analysis is given. Next, according to the concept of classical TOPSIS, the ideal and anti-ideal points of the SMADM problem are determined, which are in the form of cumulative distribution function vectors. Then, the closeness coefficient of each alternative is obtained by calculating the distances to the ideal and anti-ideal points, simultaneously. Based on the obtained closeness coefficients, a ranking of alternatives is determined. Finally, two numerical examples are given to illustrate the use of the proposed method.