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A new approach for solving intuitionistic fuzzy transportation problem of type-2

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  • Sujeet Kumar Singh

    (Indian Institute of Technology Roorkee)

  • Shiv Prasad Yadav

    (Indian Institute of Technology Roorkee)

Abstract

In solving real life transportation problem, we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representation for the data. In this paper, we formulate a transportation problem in which costs are triangular intuitionistic fuzzy numbers. We have defined accuracy function using score functions for membership and non membership functions of triangular intuitionistic fuzzy numbers. Then ordering of triangular intuitionistic fuzzy numbers using accuracy function has been proposed. We have utilized this ordering to develop methods for finding starting basic feasible solution in terms of triangular intuitionistic fuzzy numbers. Also the same ordering is utilized to develop intuitionistic fuzzy modified distribution method for finding the optimal solution. Finally the method is illustrated by a numerical example which is followed by graphical representation and discussion of the finding.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:243:y:2016:i:1:d:10.1007_s10479-014-1724-1
    DOI: 10.1007/s10479-014-1724-1
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    References listed on IDEAS

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    Cited by:

    1. P. Senthil Kumar, 2020. "Developing a New Approach to Solve Solid Assignment Problems Under Intuitionistic Fuzzy Environment," International Journal of Fuzzy System Applications (IJFSA), IGI Global, vol. 9(1), pages 1-34, January.
    2. P. Senthil Kumar, 2018. "Linear Programming Approach for Solving Balanced and Unbalanced Intuitionistic Fuzzy Transportation Problems," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 9(2), pages 73-100, April.
    3. S. K. Bharati & S. R. Singh, 2018. "A New Interval-Valued Intuitionistic Fuzzy Numbers: Ranking Methodology and Application," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 363-381, November.
    4. Priyanka Nagar & Pankaj Kumar Srivastava & Amit Srivastava, 2022. "A new dynamic score function approach to optimize a special class of Pythagorean fuzzy transportation problem," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(2), pages 904-913, June.
    5. Kuei-Hu Chang, 2019. "A novel supplier selection method that integrates the intuitionistic fuzzy weighted averaging method and a soft set with imprecise data," Annals of Operations Research, Springer, vol. 272(1), pages 139-157, January.
    6. 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.
    7. Salma Iqbal & Naveed Yaqoob & Muhammad Gulistan, 2023. "An Investigation of Linear Diophantine Fuzzy Nonlinear Fractional Programming Problems," Mathematics, MDPI, vol. 11(15), pages 1-21, August.
    8. Abdelmalek Ouannou & Adil Brouri & Laila Kadi & Hafid Oubouaddi, 2022. "Identification of switched reluctance machine using fuzzy model," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(6), pages 2833-2846, December.
    9. Sujeet Kumar Singh & Shiv Prasad Yadav, 2018. "Intuitionistic fuzzy multi-objective linear programming problem with various membership functions," Annals of Operations Research, Springer, vol. 269(1), pages 693-707, October.
    10. P. Senthil Kumar, 2020. "Intuitionistic fuzzy zero point method for solving type-2 intuitionistic fuzzy transportation problem," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 37(3), pages 418-451.
    11. P. Senthil Kumar, 2018. "A note on 'a new approach for solving intuitionistic fuzzy transportation problem of type-2'," International Journal of Logistics Systems and Management, Inderscience Enterprises Ltd, vol. 29(1), pages 102-129.
    12. Ashutosh Choudhary & Shiv Prasad Yadav, 2022. "An approach to solve interval valued intuitionistic fuzzy transportation problem of Type-2," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(6), pages 2992-3001, December.

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