| Title:
|
Eigenspace of a three-dimensional max-Łukasiewicz fuzzy matrix (English) |
| Author:
|
Rashid, Imran |
| Author:
|
Gavalec, Martin |
| Author:
|
Sergeev, Sergeĭ |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
48 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
309-328 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Eigenvectors of a fuzzy matrix correspond to stable states of a complex discrete-events system, characterized by a given transition matrix and fuzzy state vectors. Description of the eigenspace (set of all eigenvectors) for matrices in max-min or max-drast fuzzy algebra was presented in previous papers. In this paper the eigenspace of a three-dimensional fuzzy matrix in max-Łukasiewicz algebra is investigated. Necessary and sufficient conditions are shown under which the eigenspace restricted to increasing eigenvectors of a given matrix is non-empty, and the structure of the increasing eigenspace is described. Complete characterization of the general eigenspace structure for arbitrary three-dimensional fuzzy matrix, using simultaneous row and column permutations of the matrix, is presented in Sections 4 and 5, with numerical examples in Section 6. (English) |
| Keyword:
|
Łukasiewicz triangular norm |
| Keyword:
|
max-t fuzzy algebra |
| Keyword:
|
eigenproblem |
| Keyword:
|
monotone eigenvector |
| MSC:
|
62A10 |
| MSC:
|
93E12 |
| idMR:
|
MR2954329 |
| . |
| Date available:
|
2012-05-15T16:20:54Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142817 |
| . |
| Reference:
|
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