  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.
