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

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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.

Keywords

MPWC inverse / fuzzy dual number matrix equation / strong fuzzy solution / block structure

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