The relationship between attribute reducts in rough sets and minimal vertex covers of graphs

Information Sciences

Volumn 325, Issue , 2015, Pages 87-97

  Chen, Jinkun ^a   Lin, Yaojin ^a   Lin, Guoping ^a   Li, Jinjin ^a   Ma, Zhouming ^a  

^a MINNAN NORMAL UNIVERSITY   (China)

Author keywords

Attribute reduction; Graph theory; Rough sets; Vertex covers

Indexed keywords

INFORMATION SYSTEMS; INFORMATION USE; NP-HARD; ROUGH SET THEORY;

ATTRIBUTE REDUCTION; MINIMAL VERTEX COVER; VERTEX COVER; VERTEX COVER PROBLEMS;

GRAPH THEORY;

EID: 84941559911     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2015.07.008     Document Type: Article

References (68)

1. A. Bargiela, and W. Pedrycz Granular Computing: An Introduction 2003 Kluwer Academic Publishers Dordrecht
2. S.S. Bhattacharyya, S. Sriram, and E.A. Lee Resynchronization for multiprocessor DSP systems IEEE Trans. Circuits Syst I: Fundam. Theory Appl. 47 11 2000 1597 1609
3. J.A. Bondy, and U.S.R. Murty Graph Theory with Applications 1976 Elsevier Science Publishing Co., Inc.
4. J.A. Bondy, and U.S.R. Murty Graph Theory 2008 Springer Berlin
5. A. Caprara, P. Toth, D. Vigo, and M. Fischetti Modeling and solving the crew rostering problem Oper. Res. 46 6 1998 820 830
6. D.G. Chen, C.Z. Wang, and Q.H. Hu A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets Inf. Sci. 177 2007 3500 3518
7. D.G. Chen, S.Y. Zhao, L. Zhang, and et al. Sample pair selection for attribute reduction with rough set IEEE Trans. Knowledge Data Eng. 24 11 2012 2080 2093
8. D.G. Chen, and Y.Y. Yang Attribute reduction for heterogeneous data based on the combination of classical and Fuzzy rough set models IEEE Trans. Fuzzy Syst. 22 5 2014 1325 1334
9. V. Chvatal A greedy heuristic for the set-covering problem Math. Oper. Res. 4 3 1979 233 235
10. T. Eiter, and G. Gottlob Identifying the minimal transversals of a hypergraph and related problems SIAM J. Comput. 24 6 1995 1278 1304
11. F. Feng, X.Y. Liu, V. Leoreanu-Fotea, and Y.B. Jun Soft sets and soft rough sets Inf. Sci. 181 2011 1125 1137
12. F. Gavril, Private Communication cited in [14] (1974).
13. J.W. Grzymala-Busse LERS-a system for learning from examples based on rough sets R. Slowinski Intelligent Decision Support: Handbook of Applications and Advances of the Rough Set Theory 1992 Kluwer Academic Publishers 3 18
14. F.C. Gomes, C.N. Meneses, P.M. Pardalos, and G.V.R. Vianaa Experimental analysis of approximation algorithms for the vertex cover and set covering problems Comput. Oper. Res. 33 12 2006 3520 3534
15. J.W. Guan, and D.A. Bell Rough computational methods for information systems Artif. Intell. 105 1998 77 103
16. D.S. Hochbaum Efficient bounds for the stable set, vertex cover and set packing problems Discrete Appl. Math. 6 3 1983 243 254
17. D.S. Hochbaum Approximation algorithms for the set covering and vertex cover problems SIAM J. Comput. 11 3 1982 555 556
18. X.H. Hu, and N. Cercone Learning in relational databases: a rough set approach Int. J. Comput. Intell. 11 2 1995 323 338
19. Q.H. Hu, Z.X. Xie, and D.R. Yu Hybrid attribute reduction based on a novel Fuzzy-rough model and information granulation Pattern Recognit. 40 12 2007 3509 3521
20. Q.H. Hu, D.R. Yu, and M.Z. Guo Fuzzy preference based rough sets Inf. Sci. 180 2010 2003 2022
21. Q.H. Hu, D.R. Yu, W. Pedrycz, and D.G. Chen Kernelized Fuzzy rough sets and their applications IEEE Trans. Knowledge Data Eng. 23 11 2011 1649 1667
22. R.M. Karp Reducibility Among Combinatorial Problems 1972 Springer US
23. P. Kulaga, P. Sapiecha, S. Krzysztof Approximation algorithm for the argument reduction problem Computer Recognition Systems 2005 Springer Berlin 243 248
24. M. Li, C. Shang, S. Feng, and J. Fan Quick attribute reduction in inconsistent decision tables Inf. Sci. 254 2014 155 180
25. J.Y. Liang, and Z.B. Xu The algorithm on knowledge reduction in incomplete information systems Int. J. Uncertain., Fuzziness Knowl.-Based Syst. 10 1 2002 95 103
26. J.Y. Liang, and Z.Z. Shi The information entropy, rough entropy and knowledge granulation in rough set theory Int. J. Uncertain., Fuzziness Knowl.-Based Syst. 12 2004 37 46
27. P. Lingras, and C. Butz Rough set based 1-v-1 and 1-vr approaches to support vector machine multi-classification Inf. Sci. 177 18 2007 3782 3798
28. Y. Lin, J. Li, P. Lin, G. Lin, and J. Chen Feature selection via neighborhood multi-granulation fusion Knowl.-Based Syst. 67 2014 162 168
29. S. Listrovoy, and S. Minukhin The solution algorithms for problems on the minimal vertex cover in networks and the minimal cover in Boolean matrixes Int. J. Comput. Sci. Issues 9 5 2012 8 15
30. Z.Q. Meng, and Z.Z. Shi Extended rough set-based attribute reduction in inconsistent incomplete decision systems Inf. Sci. 204 2012 44 69
31. D.Q. Miao, Y. Zhao, Y.Y. Yao, and et al. Relative reducts in consistent and inconsistent decision tables of the Pawlak rough set model Inf. Sci. 179 24 2009 4140 4150
32. M. Moshkov, and M. Piliszczuk Graphical representation of information on the set of reducts, rough sets and knowledge technology Lect. Notes Comput. Sci. 4481 2007 372 378
33. M. Moshkov, A. Skowron, and Z. Suraj On covering attribute sets by reducts, rough sets and intelligent systems paradigms Lect. Notes Comput. Sci 4585 2007 175 180
34. G.L. Nemhauser, and L.E. Trotter Jr Vertex packings: structural properties and algorithms Math. Program. 8 1 1975 232 248
35. Z. Pawlak Rough sets Int. J. Comput. Inf. Sci. 5 1982 341 356
36. Z. Pawlak Rough Sets: Theoretical Aspects of Reasoning About Data 1991 Kluwer Academic Publishing Dordrecht
37. W. Pedrycz Granular Computing: Analysis and Design of Intelligent Systems 2013 CRC Press/Francis Taylor Boca Raton
38. W. Pedrycz, and W. Homendad Building the fundamentals of granular computing: a principle of justifiable granularity Appl. Soft Comput. 13 10 2013 4209 4218
39. W. Pedrycz Allocation of information granularity in optimization and decision-making models: towards building the foundations of granular computing Eur. J. Oper. Res. 232 1 2014 137 145
40. Y.H. Qian, and J.Y. Liang Combination entropy and combination granulation in rough set theory Int. J. Uncertain., Fuzziness Knowl.-Based Syst. 16 2 2008 179 193
41. Y.H. Qian, J.Y. Liang, W. Pedrycz, and C.Y. Dang Positive approximation: an accelerator for attribute reduction in rough set theory Artif. Intell. 174 9 2010 597 618
42. Y.H. Qian, S.Y. Li, J.Y. Liang, and et al. Pessimistic rough set based decisions: a multigranulation fusion strategy Inf. Sci. 264 2014 196 210
43. H.D. Sherali, and M. Rios An air force crew allocation and scheduling problem J. Oper. Res. Soc. 35 2 1984 91 103
44. W. Shu, and W. Qian A fast approach to attribute reduction from perspective of attribute measures in incomplete decision systems Know.-Based Syst. 72 2014 60 71
45. A. Skowron, and C. Rauszer The discernibility matrices and functions in information systems R. Slowinski, Intelligent Decision Support, Handbook of Applications and Advances of the Rough Sets Theory 1992 Kluwer Dordrecht
46. D. Slezak Approximate entropy reducts Fundam. Inf. 53 3-4 2002 365 390
47. B. Sun, W. Ma, and H. Zhao Decision-theoretic rough Fuzzy set model and application Inf. Sci. 283 2014 180 196
48. R.W. Swiniarski, and A. Skowron Rough set methods in feature selection and recognition Patt. Recognit. Lett. 24 6 2003 833 849
49. V.V. Vazirani Approximation Algorithms 2001 Springer Berlin
50. B. Walczak, and D.L. Massart Rough sets theory Chemometrics and Intelligent Laboratory Systems 47 1 1999 1 16
51. J. Wang, and J. Wang Reduction algorithms based on discernibility matrix: the ordered attributes method J. Comput. Sci. Technol. 16 2001 489 504
52. G.Y. Wang, J. Zhao, and J.J. An A comparative study of algebra viewpoint and information viewpoint in attribute reduction Fundam. Inf. 68 3 2005 289 301
53. F. Wang, J.Y. Liang, and C.Y. Dang Attribute reduction for dynamic data sets Appl. Soft Comput. 13 1 2013 676 689
54. C. Wang, Q. He, D. Chen, and Q. Hu A novel method for attribute reduction of covering decision systems Inf. Sci. 254 2014 181 196
55. C. Wang, M. Shao, B. Sun, and Q. Hu An improved attribute reduction scheme with covering based rough sets Appl. Soft Comput. 26 2015 235 243
56. G. Wang, H. Yu, and T. Li Decision region distribution preservation reduction in decision-theoretic rough set model Inf. Sci. 278 2014 614 640
57. G. Wang, X. Ma, and H. Yu Monotonic uncertainty measures for attribute reduction in probabilistic rough set model Int. J. Approx. Reason. 59 2015 41 67
58. Wikipedia, http://en.wikipedia.org/wiki/Hypergraph, 2015 (Last accessed 10.06.15).
59. S.K.M. Wong, and W. Ziarko On optimal decision rules in decision tables Bull. Pol. Acad. Sci. 33 1985 693 696
60. L.R. Woodyatt, K.L. Stott, F.E. Wolf, and F.J. Vasko An application combining set covering and Fuzzy sets to optimally assign metallurgical grades to customer orders Fuzzy Sets Syst. 53 1 1993 15 25
61. W.Z. Wu, M. Zhang, H.Z. Li, and J.S. Mi Knowledge reduction in random information systems via Dempster-Shafer theory of evidence Inf. Sci. 174 2005 143 164
62. S.X. Wu, M.Q. Li, W.T. Huang, and S.F. Liu An improved heuristic algorithm of attribute reduction in rough set J. Syst. Sci. Inf. 2 3 2004 557 562
63. Y.Y. Yao, and Y. Zhao Discernibility matrix simplification for constructing attribute reducts Inf. Sci. 179 7 2009 867 882
64. X. Zhang, and D. Miao Quantitative information architecture, granular computing and rough set models in the double-quantitative approximation space of precision and grade Inf. Sci. 268 2014 147 168
65. X. Zhang, and D. Miao Reduction target structure-based hierarchical attribute reduction for two-category decision-theoretic rough sets Inf. Sc. 277 2014 755 776
66. S.Y. Zhao, H. Chen, C.P. Li, M.Y. Zhai, and X.Y. Du RFRR: robust fuzzy rough reduction IEEE Trans. Fuzzy Syst. 21 5 2013 825 841
67. K. Zheng, J. Hu, Z. Zhan, J. Ma, and J. Qi An enhancement for heuristic attribute reduction algorithm in rough set Expert Syst. Appl. 41 15 2014 6748 6754
68. W. Ziarko Introduction to the special issue on rough sets and knowledge discovery Comput. Intell. 11 2 1995 223 226