# Monotone interval eigenproblem in max–min algebra

Kybernetika (2010)

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

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topGavalec, 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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- Cechlárová, K., Solutions of interval linear systems in $(max,+)$-algebra, In: Proc. 6th Internat. Symposium on Operational Research, Preddvor, Slovenia 2001, pp. 321–326.
- 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
- Cuninghame-Green, R. A., Minimax Algebra, (Lecture Notes in Economics and Mathematical Systems 166.) Springer–Verlag, Berlin 1979. Zbl0739.90073MR0580321
- Fiedler, M., Nedoma, J., Ramík, J., Rohn, J., Zimmermann, K., Linear Optimization Problems with Inexact Data, Springer–Verlag, Berlin 2006. MR2218777
- Gavalec, M., 10.1016/S0024-3795(01)00488-8, Lin. Algebra Appl. 345 (2002), 149–167. Zbl0994.15010MR1883271DOI10.1016/S0024-3795(01)00488-8
- 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
- Rohn, J., 10.1016/0024-3795(89)90004-9, Lin. Algebra Appl. 126 (1989), 39–78. Zbl1061.15003MR1040771DOI10.1016/0024-3795(89)90004-9

## Citations in EuDML Documents

top- Helena Myšková, Max-min interval systems of linear equations with bounded solution
- Helena Myšková, An iterative algorithm for testing solvability of max-min interval systems
- Helena Myšková, On an algorithm for testing T4 solvability of max-plus interval systems
- Emília Draženská, Helena Myšková, Interval fuzzy matrix equations
- Ján Plavka, Computing the greatest $\mathbf{X}$-eigenvector of a matrix in max-min algebra

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