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Solving intuitionistic fuzzy transportation problem using linear programming

Author

Listed:
  • Dalbinder Kour

    (National Institute of Technology)

  • Sathi Mukherjee

    (Gobinda Prasad Mahavidyalaya)

  • Kajla Basu

    (National Institute of Technology)

Abstract

The real life transportation problems (TP) face a lot of problems due to uncertainties and lack of precise data. The present paper focuses on the two methods for solving intuitionistic fuzzy TP. One of the methods uses intuitionistic fuzzy programming technique together with the three different membership functions—linear, exponential and hyperbolic and the other method uses crisp linear programming taking intuitionistic fuzzy data in both the methods for the cost objective functions in the TP. The first method uses the membership and non-membership degrees separately to find the crisp solution using the fuzzy programming technique and then the optimal solution is calculated in terms of intuitionistic fuzzy data with the help of defined cost membership functions using the different membership functions. The satisfaction degree is then calculated to check the better solution. The second method directly solves the TP to find crisp solution considering a single objective function. The cost objective function is taken as intuitionistic fuzzy data and the methods have been used as such for the first time. A large scale real life intuitionistic TP has been solved using the two methods. The results obtained for different membership functions have been compared.

Suggested Citation

  • Dalbinder Kour & Sathi Mukherjee & Kajla Basu, 2017. "Solving intuitionistic fuzzy transportation problem using linear programming," 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. 8(2), pages 1090-1101, November.
    • Handle: RePEc:spr:ijsaem:v:8:y:2017:i:2:d:10.1007_s13198-017-0575-y
    DOI: 10.1007/s13198-017-0575-y
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    References listed on IDEAS

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    1. Dangalchev, Chavdar Atanasov, 1996. "Partially-linear transportation problems," European Journal of Operational Research, Elsevier, vol. 91(3), pages 623-633, June.
    2. Gao, Cai & Yan, Chao & Zhang, Zili & Hu, Yong & Mahadevan, Sankaran & Deng, Yong, 2014. "An amoeboid algorithm for solving linear transportation problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 179-186.
    3. Dangalchev, Chavdar A., 2000. "Optimization of the transportation expense of a firm with contractual supplies," Transportation Research Part B: Methodological, Elsevier, vol. 34(3), pages 203-217, April.
    4. Dalbinder Kaur & Sathi Mukherjee & Kajla Basu, 2015. "Solution of a Multi-Objective and Multi-Index Real-Life Transportation Problem Using Different Fuzzy Membership Functions," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 666-678, February.
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    Cited by:

    1. P.Senthil Kumar, 2018. "PSK Method for Solving Intuitionistic Fuzzy Solid Transportation Problems," International Journal of Fuzzy System Applications (IJFSA), IGI Global, vol. 7(4), pages 62-99, October.
    2. P. Senthil Kumar, 2024. "An efficient approach for solving type-2 intuitionistic fuzzy solid transportation problems with their equivalent crisp solid transportation problems," 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. 15(9), pages 4370-4403, September.

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