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General Algebraic Solutions of Fuzzy Dual Number Linear Systems.

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Title: General Algebraic Solutions of Fuzzy Dual Number Linear Systems.
Authors: Jiang, Hongjie1 (AUTHOR), Xiao, Pengcheng2 (AUTHOR), Liu, Xiaoji3 (AUTHOR) xiaojiliu72@126.com, Habib, Mohammad Rezwan (AUTHOR) mohabib@wiley.com
Source: Journal of Applied Mathematics. 5/6/2026, Vol. 2026, p1-14. 14p.
Subjects: Linear systems, Fuzzy mathematics, Matrix inversion, Algorithms
Abstract: In this paper, we define fuzzy dual number linear systems (FDLSs) expressed as CZ˜=W˜, where C represents a crisp dual number matrix and W˜ denotes a fuzzy dual number vector. Our study focuses on three primary objectives. First, we obtain the existence of strong fuzzy solutions to the FDLS by analyzing the CMP inverse of coefficient matrix. Second, we investigate the existence of nonnegative CMP inverse by analyzing their block structure. Third, we derive general strong fuzzy solutions for the FDLS and develop a corresponding computational algorithm based on the CMP inverse. Meanwhile, a method for obtaining general solutions of the FDLS is proposed under the premise of a strong fuzzy solution. To illustrate our theoretical framework, we present numerical examples demonstrating the efficacy of the proposed methodology. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: General Algebraic Solutions of Fuzzy Dual Number Linear Systems.
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  Data: <searchLink fieldCode="AR" term="%22Jiang%2C+Hongjie%22">Jiang, Hongjie</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Xiao%2C+Pengcheng%22">Xiao, Pengcheng</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Liu%2C+Xiaoji%22">Liu, Xiaoji</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> xiaojiliu72@126.com</i><br /><searchLink fieldCode="AR" term="%22Habib%2C+Mohammad+Rezwan%22">Habib, Mohammad Rezwan</searchLink> (AUTHOR)<i> mohabib@wiley.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Applied+Mathematics%22">Journal of Applied Mathematics</searchLink>. 5/6/2026, Vol. 2026, p1-14. 14p.
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  Data: <searchLink fieldCode="DE" term="%22Linear+systems%22">Linear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Fuzzy+mathematics%22">Fuzzy mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Matrix+inversion%22">Matrix inversion</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink>
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  Label: Abstract
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  Data: In this paper, we define fuzzy dual number linear systems (FDLSs) expressed as CZ˜=W˜, where C represents a crisp dual number matrix and W˜ denotes a fuzzy dual number vector. Our study focuses on three primary objectives. First, we obtain the existence of strong fuzzy solutions to the FDLS by analyzing the CMP inverse of coefficient matrix. Second, we investigate the existence of nonnegative CMP inverse by analyzing their block structure. Third, we derive general strong fuzzy solutions for the FDLS and develop a corresponding computational algorithm based on the CMP inverse. Meanwhile, a method for obtaining general solutions of the FDLS is proposed under the premise of a strong fuzzy solution. To illustrate our theoretical framework, we present numerical examples demonstrating the efficacy of the proposed methodology. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1155/jama/9095685
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      – Code: eng
        Text: English
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        PageCount: 14
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      – SubjectFull: Linear systems
        Type: general
      – SubjectFull: Fuzzy mathematics
        Type: general
      – SubjectFull: Matrix inversion
        Type: general
      – SubjectFull: Algorithms
        Type: general
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      – TitleFull: General Algebraic Solutions of Fuzzy Dual Number Linear Systems.
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            – D: 06
              M: 05
              Text: 5/6/2026
              Type: published
              Y: 2026
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              Value: 2026
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