GAUSS−SEIDEL AND SOR METHODS FOR SOLVING INTUITIONISTIC FUZZY SYSTEM OF LINEAR EQUATIONS

Solving various real-life problems ultimately requires solving systems of linear equations. However, the parameters involved in such real-life problems may be pervaded with uncertainty, which result in fuzzy parameters rather than crisp parameters. Intuitionistic fuzzy parameters are more suitable for some cases since they allow to deal with the feeling of fear or hesitation when making a decision, which are characteristics of human being in applying knowledge and skills. Intuitionistic fuzzy linear system (IFLS) resulting from the real-life problem involves large number of equations and equally large number of unknowns. When IFLS is in matrix-vector form the resulting coefficient matrix will have a sparse structure, which makes iterative methods necessary for their solution. In this paper, the known Gauss-Seidel and SOR iterative methods for solving linear system of equations are discussed, to the best of our knowledge for the first time, to solve (IFLS). The single parametric form representation of intuitionistic fuzzy numbers (IFN) makes it possible to apply these iterative techniques to IFLS. Finally a problem of voltage input output in electric circuit has been considered to show the applicability and the efficiency of these methods.