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A Novel Ranking Approach to Solving Fully LR-Intuitionistic Fuzzy Transportation Problems

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  • Abhishekh

    (Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, Uttar Pradesh, India)

  • A. K. Nishad

    (#x2020;School of Basic and Applied Sciences, Shobhit University, Gangoh 247341 Uttar Pradesh, India)

Abstract

To the extent of our knowledge, there is no method in fuzzy environment to solving the fully LR-intuitionistic fuzzy transportation problems (LR-IFTPs) in which all the parameters are represented by LR-intuitionistic fuzzy numbers (LR-IFNs). In this paper, a novel ranking function is proposed to finding an optimal solution of fully LR-intuitionistic fuzzy transportation problem by using the distance minimizer of two LR-IFNs. It is shown that the proposed ranking method for LR-intuitionistic fuzzy numbers satisfies the general axioms of ranking functions. Further, we have applied ranking approach to solve an LR-intuitionistic fuzzy transportation problem in which all the parameters (supply, cost and demand) are transformed into LR-intuitionistic fuzzy numbers. The proposed method is illustrated with a numerical example to show the solution procedure and to demonstrate the efficiency of the proposed method by comparison with some existing ranking methods available in the literature.

Suggested Citation

  • Abhishekh & A. K. Nishad, 2019. "A Novel Ranking Approach to Solving Fully LR-Intuitionistic Fuzzy Transportation Problems," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 95-112, March.
    • Handle: RePEc:wsi:nmncxx:v:15:y:2019:i:01:n:s1793005719500066
    DOI: 10.1142/S1793005719500066
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    References listed on IDEAS

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    1. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    2. Sujeet Kumar Singh & Shiv Prasad Yadav, 2016. "A new approach for solving intuitionistic fuzzy transportation problem of type-2," Annals of Operations Research, Springer, vol. 243(1), pages 349-363, August.
    3. Abhishekh & Surendra Singh Gautam & S. R. Singh, 2018. "A Score Function-Based Method of Forecasting Using Intuitionistic Fuzzy Time Series," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 91-111, March.
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