In this paper, a fractional multi-commodity network fow problem with multi-choice parameters is studied under hybrid fuzzy-stochastic conditions. In this problem, coefcients of the objective function in both the nominator and denominator take the form of multi-choice parameters, with the alternative choices for the nominator and denominator of the fraction being represented by fuzzy-stochastic and fuzzy variables, respectively. The arc capacities are also considered as fuzzy-stochastic variables. The main goal of the present research is to provide the decision-maker with a model by the help of which he/she can manage unknown factors across a multi-commodity network. Given that this problem is herein investigated in a hybrid fuzzy-stochastic environment and includes multi-choice parameters, we use the probability-possibility approach, Lagrange interpolating polynomial, and the Charnes–Cooper variable transformation technique to convert the problem into a deterministic one. Finally, efciency of the proposed model is evaluated by presenting a couple of numerical instances.
