A Fractional Multi-commodity Network Flow Problem with Uncertain Multi-Choice Coefficients: Model Formulations and Solution Approach

In this article, a Fractional Multi-Commodity Network Flow (FMCNF) problem under uncertainty conditions will be studied. due to increasing competition in the business world, which makes decision-makers deal with multiple options/information for optimal decisions on a single task, we will look at multi-choice programming in a hybrid fuzzy random environment. The main objective of the present research is to provide the decision-maker with a model with 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 used the probability–possibility approach, Lagrange interpolating polynomial, and the Charnes-Cooper variable transformation technique to convert the problem into a deterministic one. Finally, the efficiency of the proposed model will be evaluated by presenting a numerical instance.