Further investigation to dual fuzzy matrix equation¹

Article type: Research Article

Authors: Guo, Xiaobin^{; *} | Han, Yanlong

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

Correspondence: [*] Corresponding author. Xiaobin Guo, College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China. Tel.: +861 13919030082 E-mail: guoxb@nwnu.edu.cn.

Note: [1] The work is supported by the Natural Scientific Funds of PR China (no. 61262022).

Abstract: The paper considers the general dual fuzzy matrix equation AX˜+B˜=CX˜+D˜ in a complete matrix method. We firstly introduce the fuzzy matrix and its operation with crisp number. Then we convert the dual fuzzy matrix equation to a model which is a crisp function matrix equation. The fuzzy approximate solution of dual fuzzy matrix equation is obtained by solving the model. The existence condition of the strong fuzzy solution is also discussed. In addition, we investigate the LR dual fuzzy matrix equation by the same way. Finally, some examples are given to illustrate our proposed method.

Keywords: Fuzzy numbers, fuzzy numbers matrix, dual fuzzy matrix equations, fuzzy approximate solutions

DOI: 10.3233/JIFS-17072

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 4, pp. 2617-2629, 2017