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

Kara N., KÖÇKEN H., Akdemir H. G.

Journal of Combinatorial Optimization, vol.49, no.2, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 2
  • Publication Date: 2025
  • Doi Number: 10.1007/s10878-025-01261-y
  • Journal Name: Journal of Combinatorial Optimization
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Chimica, Compendex, Computer & Applied Sciences, INSPEC, zbMATH
  • Keywords: Bisection method, Fractional programming, Fuzzy programming, Intuitionistic fuzzy number, Membership function, Multi-objective linear programming
  • Yıldız Technical University Affiliated: Yes

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.