Title: A novel technique for solving bi-level linear fractional programming problems with fuzzy interval coefficients

Authors: Nejmaddin A. Sulaiman; Gulnar W. Sadiq; Basiya K. Abdulrahim

Addresses: Department of Mathematics, College of Education, University of Salahaddin, Kurdistan Region, Iraq ' Department of Mathematics, College of Basic Education, University of Sulaimani, Kurdistan Region, Iraq ' Department of Mathematics, College of Education, University of Garmian, Kurdistan Region, Iraq

Abstract: In this paper, a bi-level linear fractional programming problem (BILLFPP) with fuzzy interval coefficient (FIC) is contemplated, where all of it is coefficients in the goal function and constraints are fuzzy intervals (FIs). Firstly, to resolve this issue, we are going to construct two LFPP with fuzzy coefficients. Before all else, of these issues is a LFPP where all of coefficients are upper approximations of FIs and the other is a LFPP where all of coefficients are lower approximations of FIs. Secondly, the BILLFPP is transformed to the form of single goal LFPP and QFPP. We address problems with a factorised or non-factorised optimisation problem and homogeneous or non-homogeneous constraints. Our proposed technique is based on a mathematical model that converts the QFPP to a LPP by solving the problem in an algebraic expression with a Taylor series. This technique, which is based on the LPP solution, can be applied to specific problems. NLFPP containing nonlinear constraints, on iterative processes, it decreases the overall processing time. Further explanations of the novel technique for solving BILLFPP are made by taking numerical examples and comparing with Jayalakshmi (2015) and Syaripuddin et al. (2017).

Keywords: LFPP; bi-level linear fractional programming problem; BILLFPP; FBILLFPP; BILLFPP with fuzzy interval; FBILLFPP with FIC; QFPP; Taylor series; a novel technique; fuzzy interval coefficient; FIC.

DOI: 10.1504/IJOR.2025.143959

International Journal of Operational Research, 2025 Vol.52 No.1, pp.99 - 115

Received: 06 May 2022
Accepted: 26 Jun 2022
Published online: 16 Jan 2025 *

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