Perturbation analysis of fully fuzzy linear systems¹

Article type: Research Article

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

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

Correspondence: [*] Corresponding author. Xiaobin Guo, College of Mathematics and Statistics, Northwest Normal University, China. Tel.: 0086 13919030082; Email: 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: This paper considers the perturbation analysis of a class of fully fuzzy linear systems in which the coefficient matrix is a positive fuzzy matrix. The original fuzzy linear systems is extended into a brand new and simple crisp matrix equation using an embedding method. By discussing the perturbation of the extended crisp linear equation, the paper completes the perturbation analysis of the original fuzzy linear system. There are three cases of perturbation are analysed and the respective relative error bounds for solutions of fuzzy linear system are derived. Some numerical examples are given to illustrated our obtained results.

Keywords: Fuzzy linear system, fuzzy solutions, matrix norm, perturbation analysis

DOI: 10.3233/JIFS-222392

Journal: Journal of Intelligent & Fuzzy Systems, vol. 44, no. 4, pp. 5589-5599, 2023