| Title:
|
A Note on Application of Two-sided Systems of $(\max , \min )$-Linear Equations and Inequalities to Some Fuzzy Set Problems (English) |
| Author:
|
Zimmermann, Karel |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
50 |
| Issue:
|
2 |
| Year:
|
2011 |
| Pages:
|
129-135 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of this short contribution is to point out some applications of systems of so called two-sided $(\max , \min )$-linear systems of equations and inequalities of [Gavalec, M., Zimmermann, K.: Solving systems of two-sided (max,min)-linear equations Kybernetika 46 (2010), 405–414.] to solving some fuzzy set multiple fuzzy goal problems. The paper describes one approach to formulating and solving multiple fuzzy goal problems. The fuzzy goals are given as fuzzy sets and we look for a fuzzy set, the fuzzy intersections of which with the fuzzy goals satisfy certain requirements concerning the heights of the intersections. Both fuzzy goals and the set to be found are supposed to have a finite support. The formulated problems can be solved by the polynomial algorithm published in [Gavalec, M., Zimmermann, K.: Solving systems of two-sided (max,min)-linear equations Kybernetika 46 (2010), 405–414.]. (English) |
| Keyword:
|
multiple fuzzy global optimization |
| Keyword:
|
$(\max , \min )$-linear equation and inequality systems |
| MSC:
|
90C26 |
| MSC:
|
90C70 |
| idZBL:
|
Zbl 1244.90259 |
| idMR:
|
MR2920715 |
| . |
| Date available:
|
2011-12-16T14:55:45Z |
| Last updated:
|
2013-09-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141761 |
| . |
| Reference:
|
[1] Bezem, M., Nieuwenhuis, R., Rodríguez-Carbonell, E.: Exponential behaviour of the Butkovič–Zimmermann algorithm for solving two-sided linear systems in max-algebra. Discrete Applied Mathematics 156 (2008), 3506–3509. Zbl 1178.68637, MR 2467321, 10.1016/j.dam.2008.03.016 |
| Reference:
|
[2] Cuninghame-Green, R. A.: Minimax Algebra. Lecture Notes in Economics and Mathematical Systems 166, Springer Verlag, Berlin, 1979. Zbl 0399.90052, MR 0580321 |
| Reference:
|
[3] Gavalec, M., Zimmermann, K.: Solving systems of two-sided (max,min)-linear equations. Kybernetika 46 (2010), 405–414. Zbl 1195.65037, MR 2676078 |
| Reference:
|
[4] Litvinov, G. L., Maslov, V. P., Sergeev, S. N.: Idempotent and Tropical Mathematics and Problems of Mathematical Physics, vol. I. Independent University Moscow, Moscow, 2007. |
| Reference:
|
[5] Maslov, V. P., Samborskij, S. N.: Idempotent Analysis. Advances in Soviet Mathematics 13, AMS, Providence, 1992. Zbl 0772.00015, MR 1203781 |
| Reference:
|
[6] Vorobjov, N. N.: Extremal algebra of positive matrices. Datenverarbeitung und Kybernetik 3 (1967), 39–71, (in Russian). MR 0216854 |
| . |
