Solving systems of two–sided (max, min)–linear equations

Martin Gavalec; Karel Zimmermann

Kybernetika (2010)

  • Volume: 46, Issue: 3, page 405-414
  • ISSN: 0023-5954

Abstract

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A finite iteration method for solving systems of (max, min)-linear equations is presented. The systems have variables on both sides of the equations. The algorithm has polynomial complexity and may be extended to wider classes of equations with a similar structure.

How to cite

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Gavalec, Martin, and Zimmermann, Karel. "Solving systems of two–sided (max, min)–linear equations." Kybernetika 46.3 (2010): 405-414. <http://eudml.org/doc/196480>.

@article{Gavalec2010,
abstract = {A finite iteration method for solving systems of (max, min)-linear equations is presented. The systems have variables on both sides of the equations. The algorithm has polynomial complexity and may be extended to wider classes of equations with a similar structure.},
author = {Gavalec, Martin, Zimmermann, Karel},
journal = {Kybernetika},
keywords = {(max; min)-linear equations; two-sided system; (max, min)-linear equations; two-sided system; finite iteration method; algorithm; polynomial complexity},
language = {eng},
number = {3},
pages = {405-414},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Solving systems of two–sided (max, min)–linear equations},
url = {http://eudml.org/doc/196480},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Gavalec, Martin
AU - Zimmermann, Karel
TI - Solving systems of two–sided (max, min)–linear equations
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 3
SP - 405
EP - 414
AB - A finite iteration method for solving systems of (max, min)-linear equations is presented. The systems have variables on both sides of the equations. The algorithm has polynomial complexity and may be extended to wider classes of equations with a similar structure.
LA - eng
KW - (max; min)-linear equations; two-sided system; (max, min)-linear equations; two-sided system; finite iteration method; algorithm; polynomial complexity
UR - http://eudml.org/doc/196480
ER -

References

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  2. Butkovič, P., Hegedüs, G., An elimination method for finding all solutions of the system of linear equations over an extremal algebra, Ekonomicko–matematický obzor 20 (1984), 203–215. MR0782401
  3. Butkovič, P., Zimmermann, K., 10.1016/j.dam.2005.09.008, Discrete Applied Mathematics 154 (2006), 437–446. MR2203194DOI10.1016/j.dam.2005.09.008
  4. Cechlárová, K., Efficient computation of the greatest eigenvector in fuzzy algebra, Tatra Mt. Math. Publications 12 (1997), 73–79. MR1607194
  5. Cechlárová, K., 10.1016/j.dam.2005.02.016, Discrete Applied Mathematics 150 (2005), Nos. 1–3, 2–15. MR2161335DOI10.1016/j.dam.2005.02.016
  6. Cuninghame-Green, R. A., Minimax Algebra, (Lecture Notes in Economics and Mathematical Systems 166.) Springer–Verlag, Berlin 1979. Zbl0739.90073MR0580321
  7. Cuninghame-Green, R. A., Butkovič, P., 10.1016/S0304-3975(02)00228-1, Theoretical Computer Science 293 (2003), 3–12. Zbl1021.65022MR1957609DOI10.1016/S0304-3975(02)00228-1
  8. Cuninghame-Green, R. A., Zimmermann, K., Equation with residual functions, Comment. Math. Univ. Carolinae 42 (2001), 729–740. MR1883381
  9. Sanchez, E., 10.1016/0165-0114(78)90033-7, Fuzzy Sets and Systems 1 (1978), 69–74. Zbl0366.04001MR0494745DOI10.1016/0165-0114(78)90033-7
  10. Sanchez, E., Inverses of fuzzy relations, Applications to possibility distributions and medical diagnosis. Fuzzy Sets and Systems 1 (1978), 75–86. Zbl0399.03040MR0521129
  11. Vorobjov, N. N., Extremal algebra of positive matrices (in Russian), Datenverarbeitung und Kybernetik 3 (1967), 39–71. MR0216854

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