The grey membership degree function is defined. As for the grey random multi-criteria decision-making problems,
in which probabilities are interval numbers and the attribute value of alternatives are interval grey numbers, a decision-making approach based on maximum membership degree is proposed. Firstly, the decision-making problem is transformed into riskfree problem by using the probability degree ranking vector of interval numbers to transform interval probabilities into point probabilities. Then the grey membership degrees of each alternative to the domain between the anti-ideal alternative and the ideal alternative are calculated, and the relative grey degrees are obtained. The order of the alternatives can be listed by comparing the grey membership degree and the relative grey degree of each alternative. Finally, an example shows the feasibility and effectiveness of this approach.