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A fuzzy approach for the intuitionistic multi-objective linear fractional programming problem using a bisection method

Author

Listed:
  • Nurdan Kara

    (National Defence University)

  • Hale Gonce Kocken

    (Yildiz Technical University)

  • Hande Günay Akdemir

    (Giresun University)

Abstract

In this paper, intuitionistic fuzzy multi-objective linear fractional programming problems (IFMOLFPs) with several fractional criteria, including profit/cost, profit/time, or profitability ratio maximization, are considered. Moreover, all parameters, with the exception of the decision variables, are characterized as triangular intuitionistic fuzzy numbers. The component-wise optimization method is employed to transform IFMOLFP into an equivalent crisp multi-objective linear fractional problem. Then, we use an iterative fuzzy methodology that integrates linear programming with a bisection approach. The proposed approach addresses single-objective and real-life multi-objective organizational planning problems, which are approached using various methods in the literature. It is used for non-linear membership functions in solving these problems. Furthermore, the values obtained using the ranking function are compared. Ultimately, the decision-maker selects the most appropriate solution technique based on the weights of the objective functions.

Suggested Citation

  • Nurdan Kara & Hale Gonce Kocken & Hande Günay Akdemir, 2025. "A fuzzy approach for the intuitionistic multi-objective linear fractional programming problem using a bisection method," Journal of Combinatorial Optimization, Springer, vol. 49(2), pages 1-24, March.
    • Handle: RePEc:spr:jcomop:v:49:y:2025:i:2:d:10.1007_s10878-025-01261-y
    DOI: 10.1007/s10878-025-01261-y
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    References listed on IDEAS

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    1. G. R. Bitran & A. G. Novaes, 1973. "Linear Programming with a Fractional Objective Function," Operations Research, INFORMS, vol. 21(1), pages 22-29, February.
    2. Sujeet Kumar Singh & Shiv Prasad Yadav, 2016. "A new approach for solving intuitionistic fuzzy transportation problem of type-2," Annals of Operations Research, Springer, vol. 243(1), pages 349-363, August.
    3. A. Charnes & W. W. Cooper, 1962. "Programming with linear fractional functionals," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 9(3‐4), pages 181-186, September.
    4. Sujeet Kumar Singh & Shiv Prasad Yadav, 2018. "Intuitionistic fuzzy multi-objective linear programming problem with various membership functions," Annals of Operations Research, Springer, vol. 269(1), pages 693-707, October.
    5. Anoop Kumar Dhingra & Moskowitz, Herbert, 1991. "Application of fuzzy theories to multiple objective decision making in system design," European Journal of Operational Research, Elsevier, vol. 53(3), pages 348-361, August.
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