Certain efficient iterative methods for bipolar fuzzy system of linear equations

Abstract

A bipolar fuzzy set model is an extension of fuzzy set model. We develop new iterative methods: generalized Jacobi, generalized Gauss-Seidel, refined Jacobi, refined Gauss-seidel, refined generalized Jacobi and refined generalized Gauss-seidel methods, for solving bipolar fuzzy system of linear equations(BFSLEs). We decompose n ×  n BFSLEs into 4n ×  4n symmetric crisp linear system. We present some results that give the convergence of proposed iterative methods. We solve some BFSLEs to check the validity, efficiency and stability of our proposed iterative schemes. Further, we compute Hausdorff distance between the exact solutions and approximate solution of our proposed schemes. The numerical examples show that some proposed methods converge for the BFSLEs, but Jacobi and Gauss-seidel iterative methods diverge for BFSLEs. Finally, comparison tables show the performance, validity and efficiency of our proposed iterative methods for BFSLEs.