On regularity of block triangular fuzzy matrices (Q1885079)
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scientific article; zbMATH DE number 2111251
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On regularity of block triangular fuzzy matrices |
scientific article; zbMATH DE number 2111251 |
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On regularity of block triangular fuzzy matrices (English)
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28 October 2004
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This paper deals with block triangular fuzzy matrices (that is, with elements in a fuzzy algebra \({\mathcal F}[0,1]\) over support \([0,1]\) with operations \(+\) and \(.\) defined as \(a+b=\max\{a,b\}\) and \(a.b=\min\{a,b\}\) for all \(a,b \in [0,1]\) and the standard order). The existence of \(\{1\}\)-inverses, semi inverses and group inverses and also the idempotence is studied for this kind of matrices. For that kind of matrices, the consistency of a fuzzy matrix equation is analyzed. Finally, Toeplitz fuzzy matrices are characterized.
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fuzzy matrix
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fuzzy relational equation
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block triangular matrix
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triangular Toeplitz matrix
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\(\{1\}\)-inverses
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semi inverses
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group inverses
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idempotence
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consistency
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