ANN Based Solution of Uncertain Linear Systems of Equations

Abstract

Linear systems of equations have many applications in the area of engineering sciences, mathematics, operations research and statistics. It is worth mentioning that the coefficient matrix of the linear systems of equations may not be always crisp due to various uncertainties. These uncertainties may be in the form of interval. Likewise, the solution set and right hand side vector may also be in interval. In this respect, a fully interval linear system of equations $(\tilde{P}\tilde{z} = \tilde{q})$ is one where the coefficient matrix, the unknown vector and the right hand side vector all are in the form of interval. Although various authors proposed different methods to handle the fully linear systems of equations but those are sometimes problem specific etc. As such, in this paper $n \times n$ fully interval linear systems of equations has been solved based on artificial neural network (ANN) model. In this regard, step by step algorithm has been included. Further, a convergence theorem has also been discussed for choosing suitable learning parameter. Few numerical examples and an application problem related to electrical circuit have been solved using the proposed method. Detail procedure has been discussed with numerical results to show the efficacy and powerfulness of the method.