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New Ranking Approach of Intuitionistic Fuzzy Sets and Its Application in Cognitive Transportation Problem

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  • Bornali Saikia

    (Sadiya College)

  • Palash Dutta

    (Dibrugarh University)

Abstract

In addressing the challenges of solving real-life transportation problems, we frequently encounter uncertainties and hesitation stemming from some uncontrollable circumstances. To cope with such challenges, various mathematical tools have been introduced by researchers. In this paper, we introduce a new ranking approach for triangular and trapezoidal intuitionistic fuzzy sets. This approach is based on the concept of degrees of membership and non-membership of intuitionistic fuzzy sets. We also include some numerical examples to demonstrate the effectiveness of our proposed ordering approach. Furthermore, we discuss on finding optimal solution of intuitionistic fuzzy transportation problems. To perform this, we have utilized this ordering approach to develop methods for finding initial basic feasible solutions and optimal solutions to transportation problems. Also, the method is elaborated by some adopted case studies which are followed by graphical representation and discussion of the observations. At length, we perform statistical tests and analyze the results to discuss the importance of our proposed approach.

Suggested Citation

  • Bornali Saikia & Palash Dutta, 2025. "New Ranking Approach of Intuitionistic Fuzzy Sets and Its Application in Cognitive Transportation Problem," SN Operations Research Forum, Springer, vol. 6(3), pages 1-46, September.
    • Handle: RePEc:spr:snopef:v:6:y:2025:i:3:d:10.1007_s43069-025-00519-9
    DOI: 10.1007/s43069-025-00519-9
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    References listed on IDEAS

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    1. P. Senthil Kumar & R. Jahir Hussain, 2016. "Computationally simple approach for solving fully intuitionistic fuzzy real life 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. 7(1), pages 90-101, December.
    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 Scientific Publishing, vol. 9(2), pages 73-100, April.
    3. Darunee Hunwisai & Poom Kumam & Wiyada Kumam, 2019. "A New Method for Optimal Solution of Intuitionistic Fuzzy Transportation Problems via Generalized Trapezoidal Intuitionistic Fuzzy Numbers," Fuzzy Information and Engineering, Taylor & Francis Journals, vol. 11(1), pages 105-120, January.
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    6. 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.
    7. Satyajit Das & Debashree Guha, 2016. "A Centroid-based Ranking Method of Trapezoidal Intuitionistic Fuzzy Numbers and Its Application to MCDM Problems," Fuzzy Information and Engineering, Taylor & Francis Journals, vol. 8(1), pages 41-74, March.
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    9. 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 Scientific Publishing, vol. 10(2), pages 20-53, April.
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