FCSTP WITH POSSIBILITY AND EXPECTED VALUE APPROACHES IN HYBRID UNCERTAIN ENVIRONMENTS

FCSTP WITH POSSIBILITY AND EXPECTED VALUE APPROACHES IN HYBRID UNCERTAIN ENVIRONMENTS

S. H. Jana, B. Jana, B. Das, G. Panirahi, M. Maiti

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Abstract

The objective of this investigation is to formulate a xed charge (FC) solid transportation problem (STP) under a hybrid uncertain environment where both fuzzi- ness 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 de- scribe 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.

Keywords

Expected value, Solid transportation problem (STP), Fuzzy rough set, Hy- brid uncertain environment, Possibility value approach.