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Hesitant intuitionistic fuzzy algorithm for multiobjective optimization problem

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  • Shailendra Kumar Bharati

    (Government Polytechnic Chunar)

Abstract

Every real-life optimization problem with uncertainty and hesitation can not be with a single objective, and consequently, a class of multiobjective linear optimization problems (MOLOP) appears in the literature. Further, the experts assign values of uncertain parameters, and the expert’s opinions about the parameters are conflicting in nature. There are concerning methods based on fuzzy sets, or their other versions are available in the literature that only covers partial uncertainty and hesitation, but the hesitant intuitionistic fuzzy sets provides a collective understanding of the real-life MOLOP under uncertainty and hesitation, and it also reflects better practical aspects of decision-making of MOLOP. In this context, the paper defines the hesitant fuzzy membership function and nonmembership function to tackle the uncertainty and hesitation of the parameters. Here, a new solution called hesitant intuitionistic fuzzy Pareto optimal solution is defined, and some theorems are stated and proved. For the decision-making of MOLOP, we develop an iterative method, and an illustrative example shows the superiority of the proposed method. And lastly, the calculated results are compared with some popular methods.

Suggested Citation

  • Shailendra Kumar Bharati, 2022. "Hesitant intuitionistic fuzzy algorithm for multiobjective optimization problem," Operational Research, Springer, vol. 22(4), pages 3521-3547, September.
    • Handle: RePEc:spr:operea:v:22:y:2022:i:4:d:10.1007_s12351-021-00685-8
    DOI: 10.1007/s12351-021-00685-8
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    References listed on IDEAS

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    1. Shailendra Kumar Bharati, 2022. "A New Interval-Valued Hesitant Fuzzy-Based Optimization Method," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 469-494, July.
    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. Zhiming Zhang, 2013. "Interval-Valued Intuitionistic Hesitant Fuzzy Aggregation Operators and Their Application in Group Decision-Making," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-33, August.
    4. 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.
    5. 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.
    6. Stanley Zionts & Jyrki Wallenius, 1976. "An Interactive Programming Method for Solving the Multiple Criteria Problem," Management Science, INFORMS, vol. 22(6), pages 652-663, February.
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