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Frontiers of Computer Science

ISSN 2095-2228

ISSN 2095-2236(Online)

CN 10-1014/TP

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2018 Impact Factor: 1.129

Front Comput Sci Chin    2011, Vol. 5 Issue (2) : 195-204    https://doi.org/10.1007/s11704-011-0331-4
RESEARCH ARTICLE
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
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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
 Cite this article:   
Xibei YANG,Ming ZHANG. Dominance-based fuzzy rough approach to an interval-valued decision system[J]. Front Comput Sci Chin, 2011, 5(2): 195-204.
 URL:  
https://academic.hep.com.cn/fcs/EN/10.1007/s11704-011-0331-4
https://academic.hep.com.cn/fcs/EN/Y2011/V5/I2/195
ua1a2a3a4a5
x1[2.17, 2.86][2.45, 2.96][5.32, 7.23][3.21, 3.95][2.54, 3.12]
x2[3.37, 4.75][3.43, 4.85][7.24, 10.47][4.00, 5.77][3.24, 4.70]
x3[1.83, 2.70][1.78, 2.98][7.23, 10.27][2.96, 4.07][2.06, 2.79]
x4[1.35, 2.12][1.42, 2.09][2.59, 3.93][1.87, 2.62][1.67, 2.32]
x5[3.46, 5.35][3.37, 5.11][6.37, 10.28][3.76, 5.70][3.41, 5.28]
x6[2.29, 3.43][2.60, 3.48][6.71, 8.81][3.30, 4.23][3.01, 3.84]
x7[2.22, 3.07][2.43, 3.32][4.37, 7.05][2.66, 3.68][2.39, 3.20]
x8[2.51, 4.04][2.52, 4.12][7.12, 11.26][4.44, 6.91][3.06, 4.65]
x9[1.24, 2.00][1.35, 1.91][3.83, 5.31][2.13, 3.01][1.72, 2.34]
x10[1.00, 1.72][1.10, 1.82][3.58, 5.65][1.67, 2.53][1.10, 1.84]
Tab.1  An interval-valued information system
x1x2x3x4x5x6x7x8x9x10
x11.000.000.001.000.000.080.380.001.000.92
x21.001.000.521.000.390.711.000.311.001.00
x30.190.001.000.810.000.000.260.000.790.98
x40.000.000.001.000.000.000.000.000.040.10
x50.850.430.441.001.000.590.900.291.001.00
x60.610.020.311.000.001.000.590.001.001.00
x70.370.000.001.000.000.071.000.000.770.73
x80.790.230.561.000.170.610.681.001.001.00
x90.000.000.000.400.000.000.000.001.000.49
x100.000.000.000.120.000.000.000.000.191.00
Tab.2  
Ua1a2a3a4a5D
x1[2.17, 2.86][2.45, 2.96][5.32, 7.23][3.21, 3.95][2.54, 3.12]2
x2[3.37, 4.75][3.43, 4.85][7.24, 10.47][4.00, 5.77][3.24, 4.70]3
x3[1.83, 2.70][1.78, 2.98][7.23, 10.27][2.96, 4.07][2.06, 2.79]1
x4[1.35, 2.12][1.42, 2.09][2.59, 3.93][1.87, 2.62][1.67, 2.32]2
x5[3.46, 5.35][3.37, 5.11][6.37, 10.28][3.76, 5.70][3.41, 5.28]3
x6[2.29, 3.43][2.60, 3.48][6.71, 8.81][3.30, 4.23][3.01, 3.84]3
x7[2.22, 3.07][2.43, 3.32][4.37, 7.05][2.66, 3.68][2.39, 3.20]3
x8[2.51, 4.04][2.52, 4.12][7.12, 11.26][4.44, 6.91][3.06, 4.65]2
x9[1.24, 2.00][1.35, 1.91][3.83, 5.31][2.13, 3.01][1.72, 2.34]1
x10[1.00, 1.72][1.10, 1.82][3.58, 5.65][1.67, 2.53][1.10, 1.84]1
Tab.3  An interval-valued decision system
x1x2x3x4x5x6x7x8x9x10
μAT? ˉ(CL1)(x)1111111111
μAT? ˉ(CL2)(x)0.81100.19110.74100
μAT? ˉ(CL3)(x)00.77000.830.390.32000
μAT?ˉ(CL1)(x)1111111111
μAT?ˉ(CL2)(x)110.81111110.400.12
μAT?ˉ(CL3)(x)0.3810.2601110.6800
μAT? ˉ(CL1)(x)000.19000000.600.88
μAT? ˉ(CL2)(x)0.6200.7410000.3211
μAT? ˉ(CL3)(x)1111111111
μAT?ˉ(CL1)(x)0.19010.81000.26011
μAT?ˉ(CL2)(x)10.23110.170.610.68111
μAT?ˉ(CL3)(x)1111111111
Tab.4  Approximate memberships for each ∈ in Table 3
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
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