Monotone interval eigenproblem in max–min algebra

Martin Gavalec; Ján Plavka

Kybernetika (2010)

  • Volume: 46, Issue: 3, page 387-396
  • ISSN: 0023-5954

Abstract

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The interval eigenproblem in max-min algebra is studied. A classification of interval eigenvectors is introduced and six types of interval eigenvectors are described. Characterization of all six types is given for the case of strictly increasing eigenvectors and Hasse diagram of relations between the types is presented.

How to cite

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Gavalec, Martin, and Plavka, Ján. "Monotone interval eigenproblem in max–min algebra." Kybernetika 46.3 (2010): 387-396. <http://eudml.org/doc/197100>.

@article{Gavalec2010,
abstract = {The interval eigenproblem in max-min algebra is studied. A classification of interval eigenvectors is introduced and six types of interval eigenvectors are described. Characterization of all six types is given for the case of strictly increasing eigenvectors and Hasse diagram of relations between the types is presented.},
author = {Gavalec, Martin, Plavka, Ján},
journal = {Kybernetika},
keywords = {(max; min) eigenvector; interval coefficients; eigenvector; interval coefficients; monotone interval eigenproblem; max-min algebra; monotone interval vector; strong eigenvector; universal eigenvector; tolerance eigenvector; interval matrix; Hasse diagram},
language = {eng},
number = {3},
pages = {387-396},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Monotone interval eigenproblem in max–min algebra},
url = {http://eudml.org/doc/197100},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Gavalec, Martin
AU - Plavka, Ján
TI - Monotone interval eigenproblem in max–min algebra
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 3
SP - 387
EP - 396
AB - The interval eigenproblem in max-min algebra is studied. A classification of interval eigenvectors is introduced and six types of interval eigenvectors are described. Characterization of all six types is given for the case of strictly increasing eigenvectors and Hasse diagram of relations between the types is presented.
LA - eng
KW - (max; min) eigenvector; interval coefficients; eigenvector; interval coefficients; monotone interval eigenproblem; max-min algebra; monotone interval vector; strong eigenvector; universal eigenvector; tolerance eigenvector; interval matrix; Hasse diagram
UR - http://eudml.org/doc/197100
ER -

References

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  1. Cechlárová, K., 10.1016/0024-3795(92)90302-Q, Lin. Algebra Appl. 175 (1992), 63–73. MR1179341DOI10.1016/0024-3795(92)90302-Q
  2. Cechlárová, K., Solutions of interval linear systems in ( max , + ) -algebra, In: Proc. 6th Internat. Symposium on Operational Research, Preddvor, Slovenia 2001, pp. 321–326. 
  3. Cechlárová, K., Cuninghame-Green, R. A., 10.1016/S0024-3795(01)00405-0, Lin. Algebra Appl. 340 (2002), 215–224. MR1869429DOI10.1016/S0024-3795(01)00405-0
  4. Cuninghame-Green, R. A., Minimax Algebra, (Lecture Notes in Economics and Mathematical Systems 166.) Springer–Verlag, Berlin 1979. Zbl0739.90073MR0580321
  5. Fiedler, M., Nedoma, J., Ramík, J., Rohn, J., Zimmermann, K., Linear Optimization Problems with Inexact Data, Springer–Verlag, Berlin 2006. MR2218777
  6. Gavalec, M., 10.1016/S0024-3795(01)00488-8, Lin. Algebra Appl. 345 (2002), 149–167. Zbl0994.15010MR1883271DOI10.1016/S0024-3795(01)00488-8
  7. Gavalec, M., Zimmermann, K., Classification of solutions to systems of two-sided equations with interval coefficients, Internat. J. Pure Applied Math. 45 (2008), 533–542. Zbl1154.65036MR2426231
  8. Rohn, J., 10.1016/0024-3795(89)90004-9, Lin. Algebra Appl. 126 (1989), 39–78. Zbl1061.15003MR1040771DOI10.1016/0024-3795(89)90004-9

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