Row Reduced Echelon Form for Solving Fully Fuzzy System with Unknown Coefficients

Ghassan Malkawi,Nazihah Ahmad,Bander Alshmari,Haslinda Ibrahim

doi:10.5899/2014/jfsva-00193

Ghassan Malkawi, Nazihah Ahmad + Show 2 more

Open Access

https://doi.org/10.5899/2014/jfsva-00193

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Abstract

This study proposes a new method for finding a feasible fuzzy solution in positive Fully Fuzzy Linear System (FFLS), where the coefficients are unknown. The fully fuzzy system is transferred to linear system in order to obtain the solution using row reduced echelon form, thereafter; the crisp solution is restricted in obtaining the positive fuzzy solution. The fuzzy solution of FFLS is included crisp intervals, to assign alternative values of unknown entries of fuzzy numbers. To illustrate the proposed method, numerical examples are solved, where the entries of coefficients are unknown in right or left hand side, to demonstrate the contributions in this study.

Highlights

Linear System of equations is considered the simplest model in solving mathematical problems
This study proposes a new method for finding a feasible fuzzy solution in positive Fully Fuzzy Linear System (FFLS), where the coefficients are unknown
The fully fuzzy system is transferred to linear system in order to obtain the solution using row reduced echelon form, thereafter; the crisp solution is restricted in obtaining the positive fuzzy solution

Summary

Introduction

Linear System of equations is considered the simplest model in solving mathematical problems. The linear system of equations are called fuzzy linear system (FLS) if the elements of the matrix in left hand side are crisp numbers and the element for vector in right hand side are represented by fuzzy numbers. Malkawi and his colleagues in [24] proposed new matrix methods for solving a positive FFLS, the necessary and sufficient condition to have a positive solution was discussed, this method capable for solving Left-Right fuzzy linear system (LR-FLS) and FLS. We propose a method that can provide a positive solution for unknown coefficients in FFLS using row reduced echelon form. A matrixwill be positive fuzzy matrix (denoted by ), if each element ofis positive We may represent such ( ̃ ̃ ̃ ) with the new notation In the rest of this paper, we will find the positive solution

The Proposed Method

Numerical examples

Conclusion