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Two stage intuitionistic fuzzy time minimizing transportation problem based on generalized Zadeh’s extension principle

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  • S. K. Bharati

    (University of Delhi)

  • Rita Malhotra

    (University of Delhi)

Abstract

In decision making of real life two stage time minimizing transportation problem (TSTMTP), we face here the state of uncertainty as well as hesitation due to some uncontrollable factors. Many authors have used fixed or fuzzy data in TSTMTP. But, TSTMTP with uncertainty and hesitation cannot be solved properly by taking fixed or fuzzy data. In present article, we have considered TSTMTP with uncertainty and hesitation of supply, demand and time. Here we have made decision of real life TSTMTP with uncertainty and hesitation by using triangular intuitionistic fuzzy numbers (TIFNs). We have generalized expected interval and value of triangular fuzzy numbers for TIFNs which converts each TIFN to a real number, also proposed and proved some related results. Further, a method is presented for the solution of real life TSTMTP and degrees of acceptance and rejection of optimal decision are computed by using generalized Zadeh’s extension principle. Finally, proposed method is implemented in an example.

Suggested Citation

  • S. K. Bharati & Rita Malhotra, 2017. "Two stage intuitionistic fuzzy time minimizing transportation problem based on generalized Zadeh’s extension principle," 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 1442-1449, November.
    • Handle: RePEc:spr:ijsaem:v:8:y:2017:i:2:d:10.1007_s13198-017-0613-9
    DOI: 10.1007/s13198-017-0613-9
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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. Aizemberg, Luiz & Kramer, Hugo Harry & Pessoa, Artur Alves & Uchoa, Eduardo, 2014. "Formulations for a problem of petroleum transportation," European Journal of Operational Research, Elsevier, vol. 237(1), pages 82-90.
    3. Das, S. K. & Goswami, A. & Alam, S. S., 1999. "Multiobjective transportation problem with interval cost, source and destination parameters," European Journal of Operational Research, Elsevier, vol. 117(1), pages 100-112, August.
    4. Abd El-Wahed, Waiel F. & Lee, Sang M., 2006. "Interactive fuzzy goal programming for multi-objective transportation problems," Omega, Elsevier, vol. 34(2), pages 158-166, April.
    5. Sharma, Anuj & Verma, Vanita & Kaur, Prabhjot & Dahiya, Kalpana, 2015. "An iterative algorithm for two level hierarchical time minimization transportation problem," European Journal of Operational Research, Elsevier, vol. 246(3), pages 700-707.
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    Cited by:

    1. 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.
    2. 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.

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