Solution of System of Linear Equations - A Neuro-Fuzzy Approach

TL;DR

This paper introduces a novel neuro-fuzzy neural network approach based on the Polak-Ribiere conjugate gradient method and fuzzy rules to solve various types of linear algebraic systems, demonstrating effective results through MATLAB simulations.

Contribution

It presents the first neuro-fuzzy model specifically designed for solving systems of linear algebraic equations, combining conjugate gradient and fuzzy learning rules.

Findings

Effective solutions for all types of linear systems

Demonstrated computational efficiency via MATLAB simulations

First application of neuro-fuzzy modeling to linear algebraic systems

Abstract

Neuro-Fuzzy Modeling has been applied in a wide variety of fields such as Decision Making, Engineering and Management Sciences etc. In particular, applications of this Modeling technique in Decision Making by involving complex Systems of Linear Algebraic Equations have remarkable significance. In this Paper, we present Polak-Ribiere Conjugate Gradient based Neural Network with Fuzzy rules to solve System of Simultaneous Linear Algebraic Equations. This is achieved using Fuzzy Backpropagation Learning Rule. The implementation results show that the proposed Neuro-Fuzzy Network yields effective solutions for exactly determined, underdetermined and over-determined Systems of Linear Equations. This fact is demonstrated by the Computational Complexity analysis of the Neuro-Fuzzy Algorithm. The proposed Algorithm is simulated effectively using MATLAB software. To the best of our knowledge this is the first work of the Systems of Linear Algebraic Equations using Neuro-Fuzzy Modeling.