Approximate calculation method of strong fuzzy solutions for fuzzy dual number matrix equations based on Moore-Penrose weak core inverse

Hongjie Jiang; Jiaying Zhu; Xianchun Meng; Hongjie Jiang; Jiaying Zhu; Xianchun Meng

doi:10.3934/era.2026289

Electronic Research Archive

2026, Volume 34, Issue 9: 6614-6635. doi: 10.3934/era.2026289

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Research article

Approximate calculation method of strong fuzzy solutions for fuzzy dual number matrix equations based on Moore-Penrose weak core inverse

1.
School of Mathematical Science, Guangxi Minzu University, Nanning 530006, Guangxi, China
2.
School of Mathematics and Physics, Hechi University, Yizhou 546300, Guangxi, China

Received: 02 April 2026 Revised: 20 June 2026 Accepted: 20 July 2026 Published: 03 August 2026

In this paper, we define fuzzy dual number matrix equations and investigate the Moore-penrose weak core inverse (MPWC inverse) to solve fuzzy dual number matrix equations. First, we define fuzzy dual number matrix equations based on the properties of fuzzy dual number. Second, we obtain the block structure of the MPWC inverse corresponding to the coefficient matrix of fuzzy dual number matrix equations by characterizing some properties of the MPWC inverse and use it to obtain a strong fuzzy solution of a fuzzy dual number matrix equation. Third, we propose two methods to derive the general strong fuzzy solution of fuzzy dual number matrix equations: one with an algorithm starting from a representation matrix obtained via the MPWC inverse, and the other starting from a representation matrix corresponding to a strong fuzzy solution. Lastly, some numerical examples are presented to illustrate the main results.
- MPWC inverse,
- fuzzy dual number matrix equation,
- strong fuzzy solution,
- block structure
Citation: Hongjie Jiang, Jiaying Zhu, Xianchun Meng. Approximate calculation method of strong fuzzy solutions for fuzzy dual number matrix equations based on Moore-Penrose weak core inverse[J]. Electronic Research Archive, 2026, 34(9): 6614-6635. doi: 10.3934/era.2026289

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Abstract

In this paper, we define fuzzy dual number matrix equations and investigate the Moore-penrose weak core inverse (MPWC inverse) to solve fuzzy dual number matrix equations. First, we define fuzzy dual number matrix equations based on the properties of fuzzy dual number. Second, we obtain the block structure of the MPWC inverse corresponding to the coefficient matrix of fuzzy dual number matrix equations by characterizing some properties of the MPWC inverse and use it to obtain a strong fuzzy solution of a fuzzy dual number matrix equation. Third, we propose two methods to derive the general strong fuzzy solution of fuzzy dual number matrix equations: one with an algorithm starting from a representation matrix obtained via the MPWC inverse, and the other starting from a representation matrix corresponding to a strong fuzzy solution. Lastly, some numerical examples are presented to illustrate the main results.

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