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

Nurdan Kara (), Hale Gonce Kocken () and Hande Günay Akdemir ()
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Nurdan Kara: National Defence University
Hale Gonce Kocken: Yildiz Technical University
Hande Günay Akdemir: Giresun University

Journal of Combinatorial Optimization, 2025, vol. 49, issue 2, No 9, 24 pages

Abstract: 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.

Keywords: Multi-objective linear programming; Fractional programming; Fuzzy programming; Intuitionistic fuzzy number; Bisection method; Membership function (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10878-025-01261-y

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