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An approach to solve interval valued intuitionistic fuzzy transportation problem of Type-2

Author

Listed:
  • Ashutosh Choudhary

    (Indian Institute of Technology)

  • Shiv Prasad Yadav

    (Indian Institute of Technology)

Abstract

In the transportation problem, transportation cost depends on several uncontrollable factors such as fluctuation in the fuel price, weather condition, road condition, etc. In most cases, exact information is utilized, but in the real world applications these quantities are imprecise and unconfirmed. Most researchers studied transportation problem with fuzzy and intuitionistic fuzzy parameters. But, both fuzzy and intuitionistic fuzzy parameters utilize fixed membership and non-membership degrees which do not deal properly with the situation of uncertainty and hesitation. Thus, we are faced with another type of ambiguity that cannot be handled by using fuzzy or intuitionistic fuzzy set. In the current work, we have designed a transportation problem in which supplies and demands are crisp numbers and costs are interval valued intuitionistic fuzzy numbers. This type of problem is termed as interval valued intuitionistic fuzzy transportation problem of Type-2. Hence, to deal with ambiguity and uncertainty in transportation problem, an algorithm is developed to find out the optimal solution of interval valued intuitionistic fuzzy transportation problem of Type-2. Finally the proposed algorithm is illustrated with the help of a numerical example and the results are compared with the existing methods.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:ijsaem:v:13:y:2022:i:6:d:10.1007_s13198-022-01771-6
    DOI: 10.1007/s13198-022-01771-6
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    References listed on IDEAS

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    1. P. Senthil Kumar, 2020. "Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set," 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. 11(1), pages 189-222, February.
    2. Ali Ebrahimnejad & Jose Luis Verdegay, 2018. "A new approach for solving fully intuitionistic fuzzy transportation problems," Fuzzy Optimization and Decision Making, Springer, vol. 17(4), pages 447-474, December.
    3. 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.
    4. 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.
    5. S. K. Bharati & S. R. Singh, 2020. "Interval-Valued Intuitionistic Fuzzy Linear Programming Problem," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 53-71, March.
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