Multi-choice Linear Programming in Fuzzy Random Hybrid Uncertainty Environment and Their Application in Multi-commodity Transportation Problem

In this paper, due to increasing competition in the business world, which makes decision makers dealing with multiple options/information for optimal decisions on a single task, we will look at multi-choice programming in hybrid fuzzy random environment. Alternative choices multi-choice parameters are considered as fuzzy random variables. By using polynomials interpolation for each multi-choice parameter, the model is transformed into a fuzzy random programming problem. Then, to convert this model to its deterministic form, we use the concept of the mean value of fuzzy random variables. Finally, to validate the proposed mathematical operations, we solve a multi-commodity transportation problem with fuzzy random multi-choice parameters.