Title: Solving bi-level linear fractional programming problems with fuzzy interval coefficients using game matrix

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 problems (BILLFPP) with fuzzy interval coefficients (FIC) was considered where all of it is coefficients in the goal function and constraints are fuzzy intervals (FIs). Firstly, to resolve this issue, we construct two LFPP with fuzzy coefficients one of these problems is a LFPP where all of it is coefficients are upper approximations of (FIs) and the other is a LFPP, where all of it is coefficients are lower approximations of (FIs) secondly, the BILLFPP are converted in to a single objective LFPP and QFPP. At the end, and we use game matrix technique which yields an efficient resolution of the original BILLFPP with fuzzy interval, the single objective LFPP or QFPP is resolved by modified simplex technique. Finally, numerical examples are given to demonstrate the results.

Keywords: LFPP; BILLFPP; FBILLFPP; BILLFPP with fuzzy interval; FBILLFPP with fuzzy interval; modified simplex technique.

DOI: 10.1504/IJMOR.2023.133716

International Journal of Mathematics in Operational Research, 2023 Vol.26 No.1, pp.19 - 36

Received: 11 May 2022
Accepted: 24 Jun 2022
Published online: 02 Oct 2023 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article