Interval fuzzy matrix equations
Emília Draženská; Helena Myšková
Kybernetika (2017)
- Volume: 53, Issue: 1, page 99-112
- ISSN: 0023-5954
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topDraženská, Emília, and Myšková, Helena. "Interval fuzzy matrix equations." Kybernetika 53.1 (2017): 99-112. <http://eudml.org/doc/287949>.
@article{Draženská2017,
abstract = {This paper deals with the solvability of interval matrix equations in fuzzy algebra. Fuzzy algebra is the algebraic structure in which the classical addition and multiplication are replaced by maximum and minimum, respectively. The notation $\mathbf \{A\} \otimes X\otimes \mathbf \{C\}=\mathbf \{B\}$, where $\mathbf \{A\}, \mathbf \{B\}, \mathbf \{C\}$ are given interval matrices and $X$ is an unknown matrix, represents an interval system of matrix equations. We can define several types of solvability of interval fuzzy matrix equations. In this paper, we shall deal with four of them. We define the tolerance, weak tolerance, left-weak tolerance, and right-weak tolerance solvability and provide polynomial algorithms for checking them.},
author = {Draženská, Emília, Myšková, Helena},
journal = {Kybernetika},
keywords = {fuzzy algebra; interval matrix equation; tolerance solvability; weak tolerance solvability},
language = {eng},
number = {1},
pages = {99-112},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Interval fuzzy matrix equations},
url = {http://eudml.org/doc/287949},
volume = {53},
year = {2017},
}
TY - JOUR
AU - Draženská, Emília
AU - Myšková, Helena
TI - Interval fuzzy matrix equations
JO - Kybernetika
PY - 2017
PB - Institute of Information Theory and Automation AS CR
VL - 53
IS - 1
SP - 99
EP - 112
AB - This paper deals with the solvability of interval matrix equations in fuzzy algebra. Fuzzy algebra is the algebraic structure in which the classical addition and multiplication are replaced by maximum and minimum, respectively. The notation $\mathbf {A} \otimes X\otimes \mathbf {C}=\mathbf {B}$, where $\mathbf {A}, \mathbf {B}, \mathbf {C}$ are given interval matrices and $X$ is an unknown matrix, represents an interval system of matrix equations. We can define several types of solvability of interval fuzzy matrix equations. In this paper, we shall deal with four of them. We define the tolerance, weak tolerance, left-weak tolerance, and right-weak tolerance solvability and provide polynomial algorithms for checking them.
LA - eng
KW - fuzzy algebra; interval matrix equation; tolerance solvability; weak tolerance solvability
UR - http://eudml.org/doc/287949
ER -
References
top- Asse, A., Mangin, P., Witlaeys, D., 10.1109/ifsa-nafips.2013.6608528, NAFIPS 2 Congress, Schenectudy 1983. DOI10.1109/ifsa-nafips.2013.6608528
- Butkovič, P., Fiedler, M., Tropical tensor product and beyond., http://web.mat.bham.ac.uk/P.Butkovic/Pubs.html.
- Cechlárová, K., Solutions of interval systems in fuzzy algebra., In: Proc. SOR 2001 (V. Rupnik, L.Zadnik-Stirn, and S. Drobne, eds.), Preddvor, pp. 321-326.
- K.Cechlárová, Cuninghame-Green, R. A., 10.1016/s0024-3795(01)00405-0, Lin. Algebra Appl. 340 (2002), 215-224. Zbl1004.15009MR1869429DOI10.1016/s0024-3795(01)00405-0
- Cuninghame-Green, R. A., 10.1007/978-3-642-48708-8, Lecture Notes in Economics and Mathematical Systems 1966, Springer, Berlin 1979. Zbl0739.90073MR0580321DOI10.1007/978-3-642-48708-8
- Gavalec, M., Plavka, J., Monotone interval eigenproblem in fuzzy algebra., Kybernetika 46 (2010), 3, 387-396. MR2676076
- Kreinovich, J., Lakeyev, A., Rohn, J., Kahl, P., 10.1007/978-1-4757-2793-7, Kluwer, Dordrecht 1998. MR1491092DOI10.1007/978-1-4757-2793-7
- Myšková, H., 10.1016/j.laa.2005.02.011, Lin. Algebra Appl. 403 (2005), 263-272. Zbl1129.15003MR2140286DOI10.1016/j.laa.2005.02.011
- Myšková, H., 10.1016/j.laa.2005.11.008, Lin. Algebra Appl. 416 (2006), 215-223. Zbl1129.15003MR2242726DOI10.1016/j.laa.2005.11.008
- Myšková, H., On an algorithm for testing T4 solvability of fuzzy interval systems., Kybernetika 48 (2012), 5, 924-938. MR3086860
- Myšková, H., 10.1016/j.laa.2015.10.031, Lin. Algebra Appl. 492 (2016), 111-127. MR3440152DOI10.1016/j.laa.2015.10.031
- Nola, A. Di, Salvatore, S., Pedrycz, W., Sanchez, E., 10.1007/978-94-017-1650-5, Kluwer Academic Publishers, Dordrecht 1989. MR1120025DOI10.1007/978-94-017-1650-5
- Plavka, J., 10.1016/j.dam.2011.11.010, Discrete Appl. Math. 160 (2012), 640-647. MR2876347DOI10.1016/j.dam.2011.11.010
- Rohn, J., Systems of Interval Linear Equations and Inequalities (Rectangular Case)., Technical Report 875, Institute of Computer Science, Academy of Sciences of the Czech Republic, Praha 2002. MR2002910
- Rohn, J., 10.1023/a:1009987227018, Reliable Computing 3 (1997), 315-323. Zbl0888.65052MR1616269DOI10.1023/a:1009987227018
- Sanchez, E., Medical diagnosis and composite relations., In: Advances in Fuzzy Set Theory and Applications (M. M. Gupta, R. K. Ragade, R. R. Yager, eds.), North-Holland, Amsterdam-New York 1979, pp. 437-444. MR0558737
- Terano, T., Tsukamoto, Y., 10.1109/cdc.1977.271521, In: Proc. IEEE Conference on Decision Control, New Orleans 1977, pp. 1390-1395. DOI10.1109/cdc.1977.271521
- Zadeh, L. A., 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.
- Zimmermann, K., Extremální algebra., Ekonomicko-matematická laboratoř Ekonomického ústavu ČSAV, Praha 1976.
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