| Title:
|
Max-min interval systems of linear equations with bounded solution (English) |
| Author:
|
Myšková, Helena |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
48 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
299-308 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Max-min algebra is an algebraic structure in which classical addition and multiplication are replaced by $\oplus$ and $\otimes$, where $a\oplus b=\max\{a,b\},\ a\otimes b=\min\{a,b\}$. The notation $\mathbf{A}\otimes \mathbf{x}=\mathbf{b}$ represents an interval system of linear equations, where $\mathbf{A}=[\underline{A},\overline{A}]$, $\mathbf{b}=[\underline{b},\overline{b}]$ are given interval matrix and interval vector, respectively, and a solution is from a given interval vector $\mathbf{x}=[\underline{x},\overline{x}]$. We define six types of solvability of max-min interval systems with bounded solution and give necessary and sufficient conditions for them. (English) |
| Keyword:
|
max-min algebra |
| Keyword:
|
interval system |
| Keyword:
|
T6-vector |
| Keyword:
|
weak T6 solvability |
| Keyword:
|
strong T6 solvability |
| Keyword:
|
T7-vector |
| Keyword:
|
weak T7 solvability |
| Keyword:
|
strong T7 solvability |
| MSC:
|
15A06 |
| MSC:
|
65G30 |
| idMR:
|
MR2954328 |
| . |
| Date available:
|
2012-05-15T16:19:44Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142816 |
| . |
| Reference:
|
[1] A. Asse, P. Mangin, D. Witlaeys: Assisted diagnosis using fuzzy information..In: NAFIPS 2 Congress, Schenectudy 1983. |
| Reference:
|
[2] K. Cechlárová: Solutions of interval systems in max-plus algebra..In: Proc. SOR 2001 (V. Rupnik, L. Zadnik-Stirn, S. Drobne, eds.), Preddvor 2001, pp. 321-326. MR 1861219 |
| Reference:
|
[3] K. Cechlárová, R. A. Cuninghame-Green: Interval systems of max-separable linear equations..Linear Algebra Appl. 340 (2002), 215-224. Zbl 1004.15009, MR 1869429 |
| Reference:
|
[4] M. Gavalec, J. Plavka: Monotone interval eigenproblem in max-min algebra..Kybernetika 46 (2010), 3, 387-396. Zbl 1202.15013, MR 2676076 |
| Reference:
|
[5] L. Hardouin, B. Cottenceau, M. Lhommeau, E. L. Corronc: Interval systems over idempotent semiring..Linear Algebra Appl. 431 (2009), 855-862. Zbl 1201.65070, MR 2535557 |
| Reference:
|
[6] H. Myšková: Interval systems of max-separable linear equations..Linear Alebra. Appl. 403 (2005), 263-272. Zbl 1129.15003, MR 2140286, 10.1016/j.laa.2005.02.011 |
| Reference:
|
[7] H. Myšková: Control solvability of interval systems of max-separable linear equations..Linear Algebra Appl. 416 (2006), 215-223. Zbl 1129.15003, MR 2242726 |
| Reference:
|
[8] H. Myšková: An algorithm for testing T4 solvability of interval systems of linear equations in max-plus algebra..In: P. 28th Internat. Scientific Conference on Mathematical Methods in Economics, České Budějovice 2010, pp. 463-468. |
| Reference:
|
[9] H. Myšková: The algorithm for testing solvability of max-plus interval systems..In: Proc. 28th Internat. Conference on Mathematical Methods in Economics, Jánska dolina 2011, accepted. |
| Reference:
|
[10] H. Myšková: Interval solutions in max-plus algebra..In: Proc. 10th Internat. Conference APLIMAT, Bratislava 2011, pp. 143-150. |
| Reference:
|
[11] A. Di Nola, S. Salvatore, W. Pedrycz, E. Sanchez: Fuzzy Relation Equations and Their Applications to Knowledge Engineering..Kluwer Academic Publishers, Dordrecht 1989. Zbl 0694.94025, MR 1120025 |
| Reference:
|
[12] J. Rohn: Systems of interval linear equations and inequalities (rectangular case)..Technical Report No. 875, Institute of Computer Science, Academy of Sciences of the Czech Republic 2002. |
| Reference:
|
[13] E. Sanchez: Medical diagnosis and composite relations..In: Advances in Fuzzy Set Theory and Applications (M. M. Gupta, R. K. Ragade, and R. R. Yager, eds.), North-Holland, Amsterdam - New York 1979, pp. 437-444. MR 0558737 |
| Reference:
|
[14] T. Terano, Y. Tsukamoto: Failure diagnosis by using fuzzy logic..In: Proc. IEEE Conference on Decision Control, New Orleans 1977, pp. 1390-1395. |
| Reference:
|
[15] L. A. Zadeh: Toward a theory of fuzzy systems..In: Aspects of Network and Systems Theory (R. E. Kalman and N. De Claris, eds.), Hold, Rinehart and Winston, New York 1971, pp. 209-245. |
| . |
