Solving fuzzy linear systems by a block representation of generalized inverse: the core inverse

This paper presents a method for solving fuzzy linear systems, where the coefficient matrix is an n × n real matrix, using a block structure of the Core inverse, and we use the Hartwig–Spindelböck decomposition to obtain the Core inverse of the coefficient matrix A . The aim of this paper is twofold...

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Bibliographic Details
Published in:Computational & applied mathematics 2020-05, Vol.39 (2), Article 133
Main Authors: Jiang, Hongjie, Wang, Hongxing, Liu, Xiaoji
Format: Article
Language:English
Subjects:
Algorithms
Applications of Mathematics
Applied physics
Coefficients
Computational mathematics
Computational Mathematics and Numerical Analysis
Fuzzy systems
Generalized inverse
Linear systems
Mathematical analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Matrix methods
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Summary:This paper presents a method for solving fuzzy linear systems, where the coefficient matrix is an n × n real matrix, using a block structure of the Core inverse, and we use the Hartwig–Spindelböck decomposition to obtain the Core inverse of the coefficient matrix A . The aim of this paper is twofold. First, we obtain a strong fuzzy solution of fuzzy linear systems, and a necessary and sufficient condition for the existence strong fuzzy solution of fuzzy linear systems are derived using the Core inverse of the coefficient matrix A . Second, general strong fuzzy solutions of fuzzy linear systems are derived, and an algorithm for obtaining general strong fuzzy solutions of fuzzy linear systems by Core inverse is also established. Finally, some examples are given to illustrate the validity of the proposed method.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-020-01156-0