The definition of interval rough stochastic variables and the arithmetic operations as well as the expected value
of interval rough stochastic numbers are given. And an interval rough operator called interval rough distance weighted
arithmetic averaging(WIRDAA) is introduced. For the problem with information of criterion weights incomplete and the
evaluation under each criterion represented as interval rough stochastic variables, a method based on WIRDAA operator is
proposed. The method calculates the expected value of variables to obtain the expected value matrix. Then a programming
model is built to get the criterion weights with the objective function of minimizing the distance. By WIRDAA operator, the
overall evaluation of each alternate is obtained, and the resulted ordering of alternates is obtained according to their overall
evaluations. Finally, an example shows the feasibility and validity of the proposed approach.