A Fixed Charge Solid Transportation Problem with Possibility and Expected Value Approaches in Hybrid Uncertain Environment

The main investigation of the paper is to develop the restricted fixed charge solid transportation problem under a hybrid uncertain environment where fuzziness and roughness coexist. A fuzzy rough STP model is developed by integrating the classical STP, fuzzy set theory, and rough set theory, which apparently provide a way to accommodate the uncertainty. For solving the problem, we apply the fuzzy rough expected value operator and propose the possibility based STP model with fuzzy rough parameters on a rough space. A numerical example is presented to describe the fuzzy rough approach using Lingo 13.0 optimization software. Finally, a graphical presentation has also shown to describe the comparison between two proposed approaches. Some important managerial decisions are also drawn by observing the optimal result.