Abstract
ABSTRACT In literature, a variety of fuzzy transportation problems are discussed and solved by defuzzification of the fuzzy input values to the crisp values. This crisp-valued conversion, in the beginning, limits the features of fuzziness as it does not take into account the uncertainties occurring in the course of intermediate calculations. The present study is a successful effort to overcome this limitation by proposing a minimum demand supply-based methodology to obtain a fuzzy initial basic feasible solution (FIBFS) of the problem. A unique ordering of trapezoidal fuzzy numbers is proposed to make the demand and supply allocation in a fuzzy form. The proposed method has been applied to a special class of fuzzy transportation problems, having all the inputs viz. demand, supply, and cost as trapezoidal fuzzy numbers. Further, the incenter fuzzy ranking process is used to convert FIBFS in a crisp initial basic feasible solution (IBFS). The optimality of the IBFS thus obtained is tested through the stepping stone method. The results obtained by the proposed approach are compared with the fuzzy Hungarian-MODI approach and the presence of inherent uncertainties in FIBFS makes the former approach superior to the latter.
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