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    • New approach for solving intuitionistic fuzzy multi-objective transportation problem

      SANKAR KUMAR ROY ALI EBRAHIMNEJAD JOSÉ LUIS VERDEGAY SUKUMAR DAS

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      Multi-objective transportation problem (MOTP) under intuitionistic fuzzy (IF) environment is analysed in this paper. Due to the fluctuation of market scenario, we assume that the transportation cost, the supply and the demand parameters are not always precise. Hence, the parameters are imprecise, i.e., they are IFnumbers. Considering the specific cut interval, the IF transportation cost matrix is converted to interval cost matrix in our proposed problem. Again, using the same concept, the IF supply and the IF demand of the MOTP are reduced to the interval form. Then the proposed MOTP is changed into the deterministic MOTP, whichincludes interval form of the objective functions. Two approaches, namely intuitionistic fuzzy programming and goal programming, are used to derive the optimal solutions of our proposed problem, and then the optimal solutions are compared. A numerical example is included to illustrate the feasibility and the applicability of the proposed problem. Finally, we present the conclusions with the future scopes of our study.

    • A new approach for solving dual-hesitant fuzzy transportation problem with restrictions

      GURUPADA MAITY DHARMADAS MARDANYA SANKAR KUMAR ROY GERHARD-WILHELM WEBER

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      This paper addresses a study on the transportation problem based on dual-hesitant fuzzy environment. The dual-hesitant fuzzy set accommodates imprecise, uncertain or incomplete information and knowledge situations in real-life operational research problems that are not possible or difficult to tackle by existing fuzzy uncertainties. Here, we present the concept of uncertainty in a transportation problem using dual-hesitant fuzzy numbers. In most of the research works, fuzzy uncertainty has been considered in transportation parameters. However, we consider the dual-hesitant fuzzy numbers to formulate a mathematical model by considering the capacity of delivering the goods by a decision maker. A special emphasis of this paper is to derive an optimal solution of transportation problem with some restrictions under uncertainty by the traditional approach (cf.Vogel’s approximation method—VAM) without using any mathematical aids. In this regard, an algorithm is developed to find the optimal solution for the dual-hesitant fuzzy transportation problem including some restrictions. Thereafter, the proposed method is illustrated by giving a numerical example for showing theeffectiveness. Finally, conclusions are given with the lines of future studies based on this paper.

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