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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Muhammad Akram & Ghulam Muhammad & Ali N. A. Koam & Nawab Hussain, 2019. "Iterative Methods for Solving a System of Linear Equations in a Bipolar Fuzzy Environment," Mathematics, MDPI, vol. 7(8), pages 1-25, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:728-:d:256427
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    References listed on IDEAS

    as
    1. Muhammad Akram & Maham Arshad, 2019. "A Novel Trapezoidal Bipolar Fuzzy TOPSIS Method for Group Decision-Making," Group Decision and Negotiation, Springer, vol. 28(3), pages 565-584, June.
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