Solving Fuzzy Linear System of Equations

محورهای موضوعی : Applied Mathematics

Mohammad Izadikhah ¹ , Alexander Graham Zikller ²

1 - Department of Mathematics, Arak Branch, Islamic Azad University, Arak, Iran
2 - Department of Mathematics, University of Mannheim, Baden-Württemberg, Germany

تاریخ دریافت : 1400/11/16 تاریخ پذیرش : 1401/01/03 تاریخ انتشار : 1400/09/10

کلید واژه: Linear system, Nearest Approximation, fuzzy data,

چکیده مقاله :

Many real problems may often be reduced to solving a system of linear equations. However, in such real-world problems, the existence of uncertainties, like a fuzzy environment, is inevitable. Thus, the main aim of this paper is to propose a solving approach for a fuzzy linear system of equalities. The presented approach is based on the nearest weighted approximation of fuzzy numbers. Two numerical examples illustrate the capabilities of the proposed approach.

منابع و مأخذ:

• Pan VY, Qian G. Randomized Preprocessing of Homogeneous Linear Systems of Equations. Linear Algebra Appl [Internet]. 2010;432(12):3272–318. Available from: https://www.sciencedirect.com/science/article/pii/S0024379510000364


• Pan VY, Qian G. Solving linear systems of equations with randomization, augmentation and aggregation. Linear Algebra Appl [Internet]. 2012;437(12):2851–76. Available from: https://www.sciencedirect.com/science/article/pii/S002437951200506X


• Kong Q, Siauw T, Bayen AM. Chapter 14 - Linear Algebra and Systems of Linear Equations. In: Kong Q, Siauw T, Bayen AMBT-PP and NM, editors. Academic Press; 2021. p. 235–63. Available from: https://www.sciencedirect.com/science/article/pii/B9780128195499000245


• Izadikhah M. A fuzzy goal programming based procedure for Machine Tool Selection. J Intell Fuzzy Syst. 2015;28(1).


• Izadikhah M, Khoshroo A. Energy management in crop production using a novel fuzzy data envelopment analysis model. RAIRO - Oper Res. 2018;52(2).


• Horčík R. Solution of a system of linear equations with fuzzy numbers. Fuzzy Sets Syst [Internet]. 2008;159(14):1788–810. Available from: https://www.sciencedirect.com/science/article/pii/S0165011408000134


• Vroman A, Deschrijver G, Kerre EE. Solving systems of linear fuzzy equations by parametric functions—An improved algorithm. Fuzzy Sets Syst [Internet]. 2007;158(14):1515–34. Available from: https://www.sciencedirect.com/science/article/pii/S0165011406005562


• Behera D, Chakraverty S. Solving fuzzy complex system of linear equations. Inf Sci (Ny) [Internet]. 2014;277:154–62. Available from: https://www.sciencedirect.com/science/article/pii/S0020025514001182


• Piegat A, Pluciński M. Application of the multidimensional RDM-arithmetic for verification of nestedness of the solution of the linear fuzzy equation system. Procedia Comput Sci [Internet]. 2021;192:533–42. Available from: https://www.sciencedirect.com/science/article/pii/S1877050921015428


• Saeidifar A. Application of weighting functions to the ranking of fuzzy numbers. Comput Math with Appl [Internet]. 2011;62(5):2246–58. Available from: http://www.sciencedirect.com/science/article/pii/S0898122111005669


• Asady B. Interval Linear Systems. Math Sci J. 2005;1(1):15–22.


• Izadikhah M, Saeidifar A, Roostaee R. Extending TOPSIS in fuzzy environment by using the nearest weighted interval approximation of fuzzy numbers. J Intell Fuzzy Syst. 2014;27:2725–2736.


• Izadikhah M, Roostaee R, Emrouznejad A. Fuzzy Data Envelopment Analysis with Ordinal and Interval Data. Int J Uncertainty, Fuzziness Knowledge-Based Syst [Internet]. 2021 May 5;29(03):385–410. Available from: https://doi.org/10.1142/S0218488521500173