Iterative Methods for Solving a System of Linear Equations in a Bipolar Fuzzy Environment

Muhammad Akram, Ghulam Muhammad, Ali N. A. Koam and Nawab Hussain
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Muhammad Akram: Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan
Ghulam Muhammad: Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan
Ali N. A. Koam: Department of Mathematics, College of Science, Jazan University, New Campus, P.O. Box 2097, Jazan 45142, Saudi Arabia
Nawab Hussain: Department of Mathematics, King Abdulaziz University, P.O Box 80203, Jeddah 21589, Saudi Arabia

Mathematics, 2019, vol. 7, issue 8, 1-25

Abstract: We develop the solution procedures to solve the bipolar fuzzy linear system of equations (BFLSEs) with some iterative methods namely Richardson method, extrapolated Richardson (ER) method, Jacobi method, Jacobi over-relaxation (JOR) method, Gauss–Seidel (GS) method, extrapolated Gauss-Seidel (EGS) method and successive over-relaxation (SOR) method. Moreover, we discuss the properties of convergence of these iterative methods. By showing the validity of these methods, an example having exact solution is described. The numerical computation shows that the SOR method with ω = 1.25 is more accurate as compared to the other iterative methods.

Keywords: BFLSEs; Jacobi and JOR iterative method; GS iterative method; EGS iterative method; SOR iterative method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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