Fuzzy probability random multi-criteria decision-making approach based on ideal-solution

Random variable with fuzzy probability and its expected value are defined. For a kind of multi-criteria decision-making problem, in which the criteria weights are precisely known and the criteria values are random variables with fuzzy probability, an approach based on ideal-solution is proposed. In this approach, first the probabilities of combined states are computed. Then through the method of ideal-solution, the relative closeness degrees of combined states are gained. Finally, the expected value of relative closeness degree is obtained to rank all the decision alternatives. An example is used to show the feasibility and availability of the method at the end of this paper.