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Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set

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  • P. Senthil Kumar

    (Navodaya Institute of Technology)

Abstract

In this article, the crisp, fuzzy and intuitionistic fuzzy optimization problem is formulated. The basic definitions and notations related to optimization problems are given in the preliminaries section. Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set is presented in this article. Then, with the help of the proposed algorithm the optimal solution of the crisp, fuzzy and intuitionistic fuzzy optimization problems are determined. A new theorem related to type-2 fuzzy/type-2 intuitionistic fuzzy optimization problems is proposed and proved. Some new and concrete results related to type-2 fuzzy/type-2 intuitionistic fuzzy optimization problems are presented. To illustrate the proposed method, some real-life numerical examples are presented. The proposed article provides seven fully worked examples with screenshots of output summaries from the software used in the computations for better understanding. The advantages of the proposed approach as compared to other existing work are also specified. Detail analyses of the comparative study as well the discussion are given. To show the advantages of the proposed approach, superiority analysis is discussed. Comparison analysis and the advantages of the proposed operators are also discussed. Some managerial applications and the advantages of the proposed approach are given. Finally, conclusion and future research directions are also given.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:ijsaem:v:11:y:2020:i:1:d:10.1007_s13198-019-00941-3
    DOI: 10.1007/s13198-019-00941-3
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    19. 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.
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    1. P. Senthil Kumar, 2019. "Intuitionistic fuzzy solid assignment problems: a software-based approach," 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. 10(4), pages 661-675, August.
    2. Shailendra Kumar Bharati, 2022. "Hesitant intuitionistic fuzzy algorithm for multiobjective optimization problem," Operational Research, Springer, vol. 22(4), pages 3521-3547, September.
    3. Oğuzhan Ahmet Arık, 2024. "Optimal policies for minimizing total job completion times and deviations from common due dates in unrelated parallel machine scheduling," OPSEARCH, Springer;Operational Research Society of India, vol. 61(3), pages 1654-1680, September.
    4. 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.
    5. 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.
    6. Zhi-Ming Chen & Cheng-Hsiung Lee & Hung-Lin Lai, 2022. "Speedup the optimization of maximal closure of a node-weighted directed acyclic graph," OPSEARCH, Springer;Operational Research Society of India, vol. 59(4), pages 1413-1437, December.
    7. Li Cheng & Liu Conglin, 2023. "Game analysis and pricing strategy of duopoly airlines based on service," 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. 14(3), pages 1103-1124, June.
    8. Saeedeh Bazari & Alireza Pooya & Omid Soleimani Fard & Pardis Roozkhosh, 2023. "Modeling and solving the problem of scheduling university exams in terms of new constraints on the conflicts of professors' exams and the concurrence of exams with common questions," OPSEARCH, Springer;Operational Research Society of India, vol. 60(2), pages 877-915, June.
    9. Namrata Rani & Vandana Goyal & Deepak Gupta, 2022. "FGP approach and Rouben ranking function to bi-level multi-objective quadratic fractional problem with trapezoidal fuzzy numbers and soft fuzzy constraints," 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(1), pages 113-122, February.
    10. P. Senthil Kumar, 2019. "PSK Method for Solving Mixed and Type-4 Intuitionistic Fuzzy Solid Transportation Problems," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 10(2), pages 20-53, April.
    11. 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.
    12. Namrata Rani & Vandana Goyal & Deepak Gupta, 2021. "A solution procedure for multi-objective fully quadratic fractional optimization 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. 12(6), pages 1447-1458, December.

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