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.
Highlights
Certain problems existing in the field of economics, social sciences and engineering involve vagueness, imprecision and uncertainty
There is a vast literature on the solution of the fuzzy system of linear equations (FSLEs) with real crisp coefficient entries and vector on the right-hand side (RHS) is parametric fuzzy numbers (PFNs) arises in many domains of technology and engineering sciences such as telecommunications, statistics, economics, social sciences, image processing and even in physics
Distance Based on Housdorff Metric. Iterative methods such as Richardson, extrapolated Richardson (ER), Jacobi, Jacobi over-relaxation (JOR), GS, extrapolated Gauss-Seidel (EGS) and successive over-relaxation (SOR) have attracted our attention to those problems which have no analytical solution in the bipolar fuzzy environment
Summary
Certain problems existing in the field of economics, social sciences and engineering involve vagueness, imprecision and uncertainty. There is a vast literature on the solution of the fuzzy system of linear equations (FSLEs) with real crisp coefficient entries and vector on the right-hand side (RHS) is parametric fuzzy numbers (PFNs) arises in many domains of technology and engineering sciences such as telecommunications, statistics, economics, social sciences, image processing and even in physics. Asady et al [24] extended the n × n FSLEs and solve it with m × n rectangular FSLEs which was introduced by Friedman, where coefficient entries are the crisp matrix and RHS functions are fuzzy number vectors. They extended the m × n original linear system into.
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