|
|
Dominance-based fuzzy rough approach to an interval-valued decision system |
Xibei YANG1,2(), Ming ZHANG1,2 |
1. School of Computer Science and Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China; 2. School of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing 210094, China |
|
|
Abstract Though the dominance-based rough set approach has been applied to interval-valued information systems for knowledge discovery, the traditional dominance relation cannot be used to describe the degree of dominance principle in terms of pairs of objects. In this paper, a ranking method of interval-valued data is used to describe the degree of dominance in the interval-valued information system. Therefore, the fuzzy rough technique is employed to construct the rough approximations of upward and downward unions of decision classes, from which one can induce at least and at most decision rules with certainty factors from the interval-valued decision system. Some numerical examples are employed to substantiate the conceptual arguments.
|
Keywords
certainty factor
decision rule
dominance relation
interval-valued information system
interval-valued decision system
fuzzy rough approximation
|
Corresponding Author(s):
YANG Xibei,Email:yangxibei@hotmail.com
|
Issue Date: 05 June 2011
|
|
1 |
Pawlak Z. Rough Sets–Theoretical Aspects of Reasoning About Data.Boston: Kluwer Academic Publishers Press, 1991
|
2 |
Greco S, Matarazzo B, S?owiński R. Rough approximation by dominance relations. International Journal of Intelligent Systems , 2002, 17(2): 153-171 doi: 10.1002/int.10014
|
3 |
Greco S, Matarazzo B, S?owiński R. Rough sets theory for multicriteria decision analysis. European Journal of Operational Research , 2001, 129(1): 1-47 doi: 10.1016/S0377-2217(00)00167-3
|
4 |
B?aszczyński J, Greco S, S?owiński R. Multi-criteria classification–a new scheme for application of dominance-based decision rules. European Journal of Operational Research , 2007, 181(3): 1030-1044 doi: 10.1016/j.ejor.2006.03.004
|
5 |
Yang X, Yang J, Wu C, Yu D. Dominance-based rough set approach and knowledge reductions in incomplete ordered information system. Information Sciences , 2008, 178(4): 1219-1234 doi: 10.1016/j.ins.2007.09.019
|
6 |
Yang X, Xie J, Song X, Yang J. Credible rules in incomplete decision system based on descriptors. Knowledge-Based Systems , 2009, 22(1): 8-17 doi: 10.1016/j.knosys.2008.04.008
|
7 |
Yang X, Yu D, Yang J, Wei L. Dominance-based rough set approach to incomplete interval-valued information system. Data & Knowledge Engineering , 2009, 68(11): 1331-1347 doi: 10.1016/j.datak.2009.07.007
|
8 |
Shao M, Zhang W. Dominance relation and rules in an incomplete ordered information system. International Journal of Intelligent Systems , 2005, 20(1): 13-27 doi: 10.1002/int.20051
|
9 |
Greco S, Inuiguchi M, S?owiński R. Fuzzy rough sets and multiple–premise gradual decision rules. International Journal of Approximate Reasoning , 2006, 41(2): 179-211 doi: 10.1016/j.ijar.2005.06.014
|
10 |
Greco S, Matarazzo B, S?owiński R. Dominance-based rough set approach to case–based reasoning. In: Proceedings of 3rd International Conference on Modeling Decisions for Artificial Intelligence. 2006, 7-18
|
11 |
Greco S, Matarazzo B, S?owiński R. Fuzzy set extensions of the dominance-based rough set approach. In: Sola H, Herrera F, Montero J, eds. Fuzzy Sets and Their Extensions: Representation, Aggregation and Models. Berlin: Springer-Verlag, 2008, 239-261
|
12 |
B?aszczyński J, Greco S, S?owiński R. On variable consistency dominance-based rough set approaches. In: Proceedings of 5th International Conference on Rough Sets and Current Trends in Computing. 2006, 191-202
|
13 |
B?aszczyński J, Greco S, S?owiński R. Monotonic variable consistency rough set approaches. In: Proceedings of 2nd International Conference on Rough Sets and Knowledge Technology. 2007, 126-133
|
14 |
Qian Y, Dang C, Liang J, Tang D. Set-valued ordered information systems. Information Sciences , 2009, 179(16): 2809-2832 doi: 10.1016/j.ins.2009.04.007
|
15 |
Fan T, Liu D, Tzeng G. Rough set-based logics for multicriteria decision analysis. European Journal of Operational Research , 2007, 182(1): 340-355 doi: 10.1016/j.ejor.2006.08.029
|
16 |
Qian Y, Liang J, Dang C. Interval ordered information systems. Computers & Mathematics with Applications , 2008, 56(8): 1994-2009 doi: 10.1016/j.camwa.2008.04.021
|
17 |
Dembczyński K, Greco S, S?owiński R. Rough set approach to multiple criteria classification with imprecise evaluations and assignments. European Journal of Operational Research , 2009, 198(2): 626-636 doi: 10.1016/j.ejor.2008.09.033
|
18 |
Da Q, Liu X. Interval number linear programming and its satisfactory solution. Systems Engineering – Theory & Practice, 1999, 19(4): 3-7
|
19 |
Facchinetti G, Ricci R, Muzzioli S. Note on ranking fuzzy triangular numbers. International Journal of Intelligent Systems , 1998, 13(7): 613-622 doi: 10.1002/(SICI)1098-111X(199807)13:7<613::AID-INT2>3.0.CO;2-N
|
20 |
Sengupta A, Pal T. On comparing interval numbers. European Journal of Operational Research , 2000, 127(1): 28-43 doi: 10.1016/S0377-2217(99)00319-7
|
21 |
Bhatt R, Gopal M. On the compact computational domain of fuzzy–rough sets. Pattern Recognition Letters , 2005, 26(11): 1632-1640 doi: 10.1016/j.patrec.2005.01.006
|
22 |
Dubois D, Prade H. Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems , 1990, 17(2): 191-209 doi: 10.1080/03081079008935107
|
23 |
Li T. Rough approximation operators on two universes of discourse and their fuzzy extensions. Fuzzy Sets and Systems , 2008, 159(22): 3033-3050 doi: 10.1016/j.fss.2008.04.008
|
24 |
Nanda S, Majumdar S. Fuzzy rough sets. Fuzzy Sets and Systems , 1992, 45(2): 157-160 doi: 10.1016/0165-0114(92)90114-J
|
25 |
Wu W, Mi J, Zhang W. Generalized fuzzy rough sets. Information Sciences , 2003, 151: 263-282 doi: 10.1016/S0020-0255(02)00379-1
|
26 |
Wu W, Zhang W. Constructive and axiomatic approaches of fuzzy approximation operators. Information Sciences , 2004, 159(3-4): 233-254 doi: 10.1016/j.ins.2003.08.005
|
27 |
Wu W, Leung Y, Mi J. On characterizations of (?,?)–fuzzy rough approximation operators. Fuzzy Sets and Systems , 2005, 154(1): 76-102 doi: 10.1016/j.fss.2005.02.011
|
28 |
Yeung D, Chen D, Tsang E, Lee J, Wang X. On the generalization of fuzzy rough sets. IEEE Transactions on Fuzzy Systems , 2005, 13(3): 343-361 doi: 10.1109/TFUZZ.2004.841734
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
|
Shared |
|
|
|
|
|
Discussed |
|
|
|
|