Comparison of Classical Method, Extension Principle and α-Cuts and Interval Arithmetic Method in Solving System of Fuzzy Linear Equations

Abstract

The system of linear equations plays a vital role in real life problems such as optimization, economics, and engineering. The parameters of the system of linear equations are modeled by taking the experimental or observation data. So the parameters of the system actually contain uncertainty rather than the crisp one. The uncertainties may be considered in term of interval or fuzzy numbers. In this paper, a detailed study of three solution techniques namely Classical Method, Extension Principle method and α-cuts and interval Arithmetic Method to solve the system of fuzzy linear equations has been done. Appropriate applications are given to illustrate each technique. Then we discuss the comparison of the different methods numerically and graphically.

Arithmetic Operations of Generalized Trapezoidal Picture Fuzzy Numbers by Vertex Method

“…Moore [6]. Then a number of researchers studied the concept of fuzzy numbers with their arithmetic operations (see [7]- [15]).…”

Linear Combination-Based Approach for Solving Imprecisely Defined Algebraic Systems of Linear Equations under Fuzzy Uncertainty

“…Inearat and Qatanani [11] also used the Jacobi, Gauss-Seidel, and successive over-relaxation iteration schemes, along with a convergence analysis for FSLE. Islam et al [12] used a matrixform method to solve the trapezoidal FSLE. Jun [13] used an approximate method with a modification of the crisp Jacobi approach in the solution process to solve the FSLE.…”