FCSTP with possibility and expected value approaches in hybrid uncertain environments

Abstract

The objective of this investigation is to formulate a fixed charge (FC) solid transportation problem (STP) under a hybrid uncertain environment where both 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 provides 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. At the end, a mathematical illustration is provided to describe the fuzzy rough approach using LINGO 14.0 optimization software. As particular cases, the proposed model is also solved for single impreciseness. Finally, a graphical presentation is also shown to describe the comparison between two proposed approaches. In a particular case, the expressions of an earlier investigator have been derived from the present expressions. Important managerial decisions are made after observation of optimal results.