Generalized fuzzy eigenvectors of real symmetric matrices¹

Article type: Research Article

Authors: Guo, Xiaobin^{; *} | Chen, Ying | Zhuo, Quanxiu

Affiliations: College of Mathematics and Statistics, Northwest Normal University, China

Correspondence: [*] Corresponding authors. Xiaobin Guo, College of Mathematics and Statistics, Northwest Normal University, China. Tel.: 0086 13919030082; E-mail: guoxb@nwnu.edu.cn.

Note: [1] The work is supported by the Natural Scientific Funds of PR China (no . 61967014, 11861059) and the Natural Scientific Funds of Gansu Province (no . 20JR10RA101).

Abstract:  In paper the generalized real eigenvalue and fuzzy eigenvector of a crisp real symmetric matrix with respect to another real symmetric matrix is studied. The original generalized fuzzy eigen problem is extended into a crisp generalized eigen problem of a real symmetric matrix with high orders using the arithmetic operation of LR fuzzy matrix and vector. Two cases are analysed: (a) the unknown eigenvalue λ is a non negative real number; (b) the unknown eigenvalue λ is a negative real number. Two computing models are established and an algorithm for finding the generalized fuzzy eigenvector of a real symmetric matrix is derived. Moreover, a sufficient condition for the existence of a strong generalized fuzzy eigenvector is given. Some numerical examples are shown to illustrated our proposed method.

Keywords: Fuzzy numbers, fuzzy eigenvectors, matrix computation, fuzzy linear systems

DOI: 10.3233/JIFS-222641

Journal: Journal of Intelligent & Fuzzy Systems, vol. 44, no. 5, pp. 7459-7467, 2023