Maximal solutions of two–sided linear systems in max–min algebra
Pavel Krbálek; Alena Pozdílková
Kybernetika (2010)
- Volume: 46, Issue: 3, page 501-512
- ISSN: 0023-5954
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topKrbálek, Pavel, and Pozdílková, Alena. "Maximal solutions of two–sided linear systems in max–min algebra." Kybernetika 46.3 (2010): 501-512. <http://eudml.org/doc/196920>.
@article{Krbálek2010,
abstract = {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.},
author = {Krbálek, Pavel, Pozdílková, Alena},
journal = {Kybernetika},
keywords = {max-min algebra; two-sided linear systems; lower bound; upper bound; max-min algebra; two-sided linear systems; lower bound; upper bound; maximal solution; polynomial algorithm; complexity},
language = {eng},
number = {3},
pages = {501-512},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Maximal solutions of two–sided linear systems in max–min algebra},
url = {http://eudml.org/doc/196920},
volume = {46},
year = {2010},
}
TY - JOUR
AU - Krbálek, Pavel
AU - Pozdílková, Alena
TI - Maximal solutions of two–sided linear systems in max–min algebra
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 3
SP - 501
EP - 512
AB - 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.
LA - eng
KW - max-min algebra; two-sided linear systems; lower bound; upper bound; max-min algebra; two-sided linear systems; lower bound; upper bound; maximal solution; polynomial algorithm; complexity
UR - http://eudml.org/doc/196920
ER -
References
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- Gavalec, M., Zimmermann, K., Solving systems of two-sided (max,min)-linear equations, Kybernetika 46 (2010), 405–414. Zbl1195.65037MR2676078
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