Accelerated overrelaxation (AOR) method in solving fuzzy system of linear equations

Kalawathi Govindaraj, (2007) Accelerated overrelaxation (AOR) method in solving fuzzy system of linear equations. Universiti Malaysia Sabah. (Unpublished)

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Abstract

In most of the science and engineering field, the linear system plays a very essential role, mainly in the applications sectors. However, several of the applications use fuzzy numbers rather than the crisp number for the precision reason. Thus, it is very important to develop numerical procedures that can appropriately solve general fuzzy linear systems. This study was carried out with the objective to propose the Accelerated Overrelaxation (AOR) algorithm for solving mainly the Fuzzy System of Linear Equations (FSLE). FSLE was derived into matrix notation using the embedding method. Embedding method facilitates to extend the fuzzy linear system into crisp linear system where the generated matrix size will be double the size of the original fuzzy linear system. In this study, only square matrices were taken into consideration. The extended matrices were solved using the control method, Gauss Seidel (GS) and the proposed method, AOR method. By substituting appropriate values for all the parameters involved such as the overrelaxation parameter and acceleration parameter, the optimal solutions were obtained for both control and proposed methods. These two methods were also compared in the aspects of number of iterations and execution time. Based on the results, it was concluded that AOR method converges faster with lesser number of iterations and execution time than the GS method with a better convergence rate.

Item Type: Academic Exercise
Uncontrolled Keywords: linear system, fuzzy number, Accelerated Overrelaxation algorithm, Fuzzy System of Linear Equation, GS method
Subjects: Q Science > QA Mathematics
Divisions: SCHOOL > School of Science and Technology
Depositing User: MDM SITI AZIZAH IDRIS
Date Deposited: 07 Jan 2014 08:07
Last Modified: 10 Oct 2017 08:21
URI: http://eprints.ums.edu.my/id/eprint/7992

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