Stochastic multi-attribute decision-making model based on grey matrix relational analysis and its application

In this paper, a method based on grey matrix relational analysis is proposed for stochastic multi-attribute decision-making (SMADM) problem which features incomplete information on attribute's weights and attribute values in terms of random variables which obey normal distribution. Firstly, on the basis of analyzing the related property of normal distribution, we design an index-preference probability matrix to distinguish different alternatives. A single objective programming model based on the deviation maximization theory among attributes is developed to determine the optimal weight vector. Secondly, according to grey matrix relational degree, alternatives are ranked and the complete order is obtained. Finally, a practical example is used to show the feasibility and validity of this method.