| Title:
|
Maximal solutions of two–sided linear systems in max–min algebra (English) |
| Author:
|
Krbálek, Pavel |
| Author:
|
Pozdílková, Alena |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
46 |
| Issue:
|
3 |
| Year:
|
2010 |
| Pages:
|
501-512 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Max-min algebra and its various aspects have been intensively studied by many authors [1, 4] because of its applicability to various areas, such as fuzzy system, knowledge management and others. Binary operations of addition and multiplication of real numbers used in classical linear algebra are replaced in max-min algebra by operations of maximum and minimum. We consider two-sided systems of max-min linear equations $A \otimes x = B \otimes x$, with given coefficient matrices $A$ and $B$. We present a polynomial method for finding maximal solutions to such systems, and also when only solutions with prescribed lower and upper bounds are sought. (English) |
| Keyword:
|
max-min algebra |
| Keyword:
|
two-sided linear systems |
| Keyword:
|
lower bound |
| Keyword:
|
upper bound |
| MSC:
|
08A72 |
| MSC:
|
15A06 |
| MSC:
|
15A24 |
| MSC:
|
15A80 |
| idZBL:
|
Zbl 1204.15008 |
| idMR:
|
MR2676086 |
| . |
| Date available:
|
2010-09-13T17:00:52Z |
| Last updated:
|
2013-09-21 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140764 |
| . |
| Reference:
|
[1] Baccelli, F. L., Cohen, G., Olsder, G. J., Quadrat, J. P.: Synchronization and Linearity.An Algebra for Discrete Event Systems. Wiley, Chichester 1992. Zbl 0824.93003, MR 1204266 |
| Reference:
|
[2] Butkovič, P., Zimmermann, K.: A strongly polynomial algorithm for solving two-sided systems of (max,plus)-linear equations.Discrete Applied Math. 154 (2006), 437–446. MR 2203194, 10.1016/j.dam.2005.09.008 |
| Reference:
|
[3] Cechlárová, K., Cuninghame-Green, R. A.: Interval systems of max-separable linear equations.Linear Algebra Appl. 340 (2002), 215–224. MR 1869429 |
| Reference:
|
[4] Cunninghame-Green, R. A.: Minimax Algebra.(Lecture Notes in Economy and Mathematical Systems 166.) Springer-Verlag, Berlin 1979. MR 0580321 |
| Reference:
|
[5] Gavalec, M., Zimmermann, K.: Solving systems of two-sided (max,min)-linear equations.Kybernetika 46 (2010), 405–414. Zbl 1195.65037, MR 2676078 |
| Reference:
|
[6] Sanchez, E.: Resolution of eigen fuzzy sets equations.Fuzzy Sets and System 1 (1978), 69–74. Zbl 0366.04001, MR 0494745, 10.1016/0165-0114(78)90033-7 |
| . |
