In this paper, we first introduce a new category of mathematical programming where the problem coefficients are interval random variables. These problems include two different kinds of ambiguity in the problem coefficients which are being interval and being random. We use Fractile method to solve these problems. In this method, using the existing method, we change the interval problem coefficients to random mode and then we solve the random problem using Fractile method. Also, a numerical example is presented to show the effectiveness of this model. Finally, we emphasize that this approach can be useful for the model with multi-objective as a generalized model in the future study. Manuscript profile

This paper seeks to address the multi-commodity flow problem in uncertainty conditions, in which the objective function of the problem is of fractional type. The cost coefficients and capacities of the problem are uncertain. The purpose of using uncertainty theory is to deal with unknown factors in the uncertain network. After stating the optimality conditions, the problem is transformed into a certain fractional multi-commodity flow problem by applying the uncertain chance-constrained programming approach. Then, the variable transformation approach is used to transform the nonlinear objective function to its linear form. Finally, two numerical examples are evaluated to verify the efficiency of the proposed formulation. Manuscript profile