For the random multi-criteria decision-making problem, in which the information on criteria’s weights is incomplete and the criteria value of alternatives are in the form of interval intuitionistic fuzzy numbers, an intuitionistic random multi-criteria decision-making approach based on score function is proposed. First, discrete interval intuitionistic random variable, a new score function, the expected score value and score standard deviation of interval intuitionistic random variable are defined。After that, by using the incomplete certain information of criteria weight coefficient, the optimized linear programming model based on the expected score value of alternatives is constructed. The optimal criteria weights can be gained by solving the model, and a distribution of union intuitionistic random variable for each alternative can be figured out. Then, comprehensive score standard expected value for each alternative can be obtained according to the distribution.
With the adoption of the calculation method of probability degree of interval numbers, the evaluation matrix of the range of comprehensive evaluation for alternatives can be enacted and the order of the alternatives can be listed. Finally, an example shows the feasibility and validity of this approach.