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

Nejmaddin A. Sulaiman, Gulnar W. Sadiq and Basiya K. Abdulrahim

International Journal of Mathematics in Operational Research, 2023, vol. 26, issue 1, 19-36

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. (search for similar items in EconPapers)
Date: 2023
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