| Title:
|
Solving systems of two–sided (max, min)–linear equations (English) |
| Author:
|
Gavalec, Martin |
| Author:
|
Zimmermann, Karel |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
46 |
| Issue:
|
3 |
| Year:
|
2010 |
| Pages:
|
405-414 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
(max,min)-linear equations |
| Keyword:
|
two-sided system |
| MSC:
|
08A72 |
| MSC:
|
15A06 |
| MSC:
|
15A80 |
| MSC:
|
15B15 |
| MSC:
|
65F10 |
| MSC:
|
65Y20 |
| MSC:
|
90B35 |
| MSC:
|
90C47 |
| idZBL:
|
Zbl 1195.65037 |
| idMR:
|
MR2676078 |
| . |
| Date available:
|
2010-09-13T16:49:21Z |
| Last updated:
|
2013-09-21 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140756 |
| . |
| Reference:
|
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| Reference:
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| Reference:
|
[3] Butkovič, P., Zimmermann, K.: A strongly polynomial algorithm for solving two-sided linear systems in max-algebra.Discrete Applied Mathematics 154 (2006), 437–446. MR 2203194, 10.1016/j.dam.2005.09.008 |
| Reference:
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| Reference:
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| Reference:
|
[6] Cuninghame-Green, R. A.: Minimax Algebra.(Lecture Notes in Economics and Mathematical Systems 166.) Springer–Verlag, Berlin 1979. Zbl 0739.90073, MR 0580321 |
| Reference:
|
[7] Cuninghame-Green, R. A., Butkovič, P.: The equation $A \otimes x = B \otimes y$ over (max,+).Theoretical Computer Science 293 (2003), 3–12. Zbl 1021.65022, MR 1957609, 10.1016/S0304-3975(02)00228-1 |
| Reference:
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| Reference:
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[9] Sanchez, E.: Resolution of eigen fuzzy sets equations.Fuzzy Sets and Systems 1 (1978), 69–74. Zbl 0366.04001, MR 0494745, 10.1016/0165-0114(78)90033-7 |
| Reference:
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[10] Sanchez, E.: Inverses of fuzzy relations.Applications to possibility distributions and medical diagnosis. Fuzzy Sets and Systems 1 (1978), 75–86. Zbl 0399.03040, MR 0521129 |
| Reference:
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| . |
