Research ArticleOpen AccessGoogle Scholar indexed

Comparison of Classical Method, Extension Principle and α-Cuts and Interval Arithmetic Method in Solving System of Fuzzy Linear Equations

¹ Department of Mathematics, IUBAT (International University of Business Agriculture and Technology), Dhaka, Bangladesh
² Department of Mathematics, IUBAT (International University of Business Agriculture and Technology), Dhaka, Bangladesh
³ Department of Mathematics, IUBAT (International University of Business Agriculture and Technology), Dhaka, Bangladesh
⁴ Department of Mathematics, Jahangirnagar University, Dhaka, Bangladesh

American Journal of Computational Mathematics·Volume 09 (2019)·Pages 1–24·Published 1 March 2019·DOI10.4236/ajcm.2019.91001

Abstract

The system of linear equations plays a vital role in real life problems such as optimization, economics, and engineering. The parameters of the system of linear equations are modeled by taking the experimental or observation data. So the parameters of the system actually contain uncertainty rather than the crisp one. The uncertainties may be considered in term of interval or fuzzy numbers. In this paper, a detailed study of three solution techniques namely Classical Method, Extension Principle method and α-cuts and interval Arithmetic Method to solve the system of fuzzy linear equations has been done. Appropriate applications are given to illustrate each technique. Then we discuss the comparison of the different methods numerically and graphically.

KeywordsFuzzy SetClassical SolutionExtension Principleα-Cut and Interval Arithmetic Method

Moore, R.E. (1979) Methods and Applications of Interval Analysis. SIAM, Philadelphia. https://doi.org/10.1137/1.9781611970906
Allahviranloo, T., Salahshour, S., Homayoun-nejad, M. and Baleanu, D. (2013) General Solutions of Fully Fuzzy Linear System. General Solutions of Fully Fuzzy Linear System, 2013, Article ID: 593274. https://doi.org/10.1155/2013/593274
Friedman, M., Ma, M. and Kandel, A. (1998) Fuzzy Linear Systems. Fuzzy Sets and Systems, 96, 201-209. https://doi.org/10.1016/S0165-0114(96)00270-9
Allahviranloo, T. (2004) Numerical Methods for Fuzzy System of Linear Equations. Applied Mathematics and Computation, 155, 493-502. https://doi.org/10.1016/S0096-3003(03)00793-8
Allahviranloo, T. (2005) Successive over Relaxation Iterative Method for a Fuzzy System of Linear Equations. Applied Mathematics and Computation, 162, 189-196. https://doi.org/10.1016/j.amc.2003.12.085
Allahviranloo, T. (2005) The Adomian Decomposition Method for a Fuzzy System of Linear Equations. Applied Mathematics and Computation, 163, 553-563. https://doi.org/10.1016/j.amc.2004.02.020
Allahviranloo, T., Ahmady, E., Ahmady, N. and Shams Alketaby, Kh. (2006) Block Jacobi Two-Stage Method with Gauss-Sidel Inner Iterations for Fuzzy System of Linear Equations. Applied Mathematics and Computation, 175, 1217-1228. https://doi.org/10.1016/j.amc.2005.08.047
Dehghan, M., Hashemi, B. and Ghatee, M. (2007) Solution of the Fully Fuzzy Linear Systems Using Iterative Techniques. Chaos Solutions and Fractals, 34, 316-336. https://doi.org/10.1016/j.chaos.2006.03.085
Dehghan, M. and Hashemi, B. (2006) Solution of the Fully Fuzzy Linear Systems Using the Decomposition Procedure. Applied Mathematics and Computation, 182, 1568-1580. https://doi.org/10.1016/j.amc.2006.05.043
Ming, M., Friedman, M. and Kandel, A. (1997) General Fuzzy Least Squares. Fuzzy Sets and Systems, 88, 107-118. https://doi.org/10.1016/S0165-0114(96)00051-6
Klir, G.J. (2013) Lotfi Zadeh, Fuzzy Sets, and I: A Personal Odyssey. In: Seising R., Trillas, E., Moraga, C. and Termini, S., Eds., On Fuzziness. Studies in Fuzziness and Soft Computing, Vol. 298, Springer, Berlin, Heidelberg.
Buckley, J.J. (1992) Solving Fuzzy Equations. Fuzzy Sets and Systems, 50, 1-14. https://doi.org/10.1016/0165-0114(92)90199-E

Menu

Menu

Menu

Comparison of Classical Method, Extension Principle and α-Cuts and Interval Arithmetic Method in Solving System of Fuzzy Linear Equations

Abstract

References (12)