Numerical Solution of Interval and Fuzzy System of Linear Equations

A system of linear equations, in general is solved in open literature for crisp unknowns, but in actual case the parameters (coefficients) of the system of linear equations contain uncertainty and are less crisp. The uncertainties may be considered in term of interval or fuzzy number. In this paper, a detail of study of linear simultaneous equations with interval and fuzzy parameter (triangular and trapezoidal) has been performed. New methods have been proposed for solving such systems. First, the methods have been tested for known problems viz. a circuit analysis solved in the literature and the results are found to be in good agreement with the present. Next more example problems are solved using the proposed methods to strengthen confidence on these new methods. The solutions of the example problems clearly show the efficacy and reliability of the proposed method(s)

Solution of Fuzzy System of Linear Equations with Polynomial Parametric Form

This paper proposed two new and simple solution methods to solve a fuzzy system of linear equations having fuzzy coefficients and crisp variables using a polynomial parametric form of fuzzy numbers. Related theorems are stated and proved. The proposed methods are used to solve example problems. The results obtained are also compared with the known solutions and are found to be in good agreement

A Proposed Method for Solving Fuzzy System of Linear Equations

This paper proposes a new method for solving fuzzy system of linear equations with crisp coefficients matrix and fuzzy or interval right hand side. Some conditions for the existence of a fuzzy or interval solution of × linear system are derived and also a practical algorithm is introduced in detail. The method is based on linear programming problem. Finally the applicability of the proposed method is illustrated by some numerical examples