Numerical solution of interval and fuzzy system of linear equations

Abstract

The system of linear equation has a great importance in many real life problem such as economics, Optimization and in various engineering field. We know that system of linear equations, in general is solved for crisp unknowns. For the sake of simplicity or for fuzzy computation it is taken as crisp value. In actual case 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 number.

Recently different authors have investigated these problems by various methods. These methods are described for the system having various type of fuzzy and non-fuzzy parameters. Although solutions are obtained by these methods are good but sometimes the method requires lengthy procedure and computationally not efficient.

Here, in this thesis detail study of linear simultaneous equations with interval and fuzzy parameter have been done. New methods have been proposed for the same.

The proposed 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 have confidence on these new methods. There exists various type of fuzzy numbers. As such here the problems are also been solved by two types of fuzzy numbers. Corresponding plots of the solution for all the example problems are included in this thesis.

In view of the above analysis of the results, it is found that the proposed methods are simple and computationally efficient.