Probabilistic rough set approximations

International Journal of Approximate Reasoning

Volumn 49, Issue 2, 2008, Pages 255-271

  Yao, Yiyu ^a  

^a UNIVERSITY OF REGINA   (Canada)

Author keywords

Approximation operators; Decision theoretic model; Probabilistic rough set models; Rough sets; Variable precision and parameterized models

Indexed keywords

DECISION THEORY; FUZZY SETS; INFORMATION THEORY; MEMBERSHIP FUNCTIONS; PROBABILITY; RISK ASSESSMENT; SET THEORY;

APPROXIMATION OPERATORS; BAYESIAN DECISION; CRITICAL REVIEW; DECISION-THEORETIC; DECISION-THEORETIC MODEL; INCLUSION FUNCTIONS; INFORMATION-THEORETIC ANALYSIS; NEW RESULTS; PROBABILISTIC APPROACHES; PROBABILISTIC ROUGH SET MODELS; ROUGH MEMBERSHIP; ROUGH SET APPROXIMATION; ROUGH SET MODELS; ROUGH SETS; SYSTEMATIC METHODS; VARIABLE PRECISION AND PARAMETERIZED MODELS; VARIABLE PRECISIONS;

ROUGH SET THEORY;

EID: 52949144505     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2007.05.019     Document Type: Article

References (69)

1. M.M.E. Abd El-Monsef, N.M. Kilany, Decision analysis via granulation based on general binary relation, International Journal of Mathematics and Mathematical Sciences 2007 (2007), doi:10.1155/2007/12714. Available at .
2. R. Agrawal, T. Imielinski, A. Swami, Mining association rules between sets of items in large databases, in: Proceedings of ACM Special Interest Group on Management of Data, 1993, pp. 207-216.
3. Beauboef T., Petry F.E., and Arora G. Information-theoretic measures of uncertainty for rough sets and rough relational databases. Information Sciences 109 (1998) 185-195
4. Bryniarski E., and Wybraniec-Skardowska U. Generalized rough sets in contextual space. In: Lin T.Y., and Cercone N. (Eds). Rough Sets and Data Mining (1997), Kluwer Academic Publishers, Boston 339-354
5. Deogun J.S., Raghavan V.V., Sarkar A., and Sever H. Data mining: trends in research and development. In: Lin T.Y., and Cercone N. (Eds). Rough Sets and Data Mining (1997), Kluwer Academic Publishers, Boston 9-45
6. J.S. Deogun, V.V. Raghavan, H. Sever, Rough set based classification methods and extended decision tables, in: Proceedings of the International Workshop on Rough Sets and Soft Computing, RSSC'04, 1994, pp. 302-309.
7. Duda R.O., and Hart P.E. Pattern Classification and Scene Analysis (1973), Wiley, New York
8. Düntsch I., and Gediga G. Roughian: rough information analysis. International Journal of Intelligent Systems 16 (2001) 121-147
9. Eells E., and Fitelson B. Symmetries and asymmetries in evidential support. Philosophical Studies 107 (2002) 129-142
10. Fattorosi-Barnaba M., and Amati G. Modal operators with probabilistic interpretations I. Studia Logica XLVI (1987) 383-393
11. S. Greco, B. Matarazzo, R. Sowiński, Rough membership and Bayesian confirmation measures for parameterized rough sets, in: Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, Proceedings of RSFDGrC'05, LNAI, vol. 3641, 2005, pp. 314-324.
12. S. Greco, B. Matarazzo, R. Słowiński, Parameterized rough set model using rough membership and Bayesian confirmation measures, International Journal of Approximate Reasoning, (2007), in press, doi:10.1016/j.ijar.2007.05.018.
13. Grzymala-Busse J.W. LERS - a system for learning from example based on rough sets. In: Słowiński R. (Ed). Intelligent Support: Handbook of Applications and Advances of the Rough Set Theory (1992), Kluwer Academic Publishers, Dordrecht 3-18
14. Katzberg J.D., and Ziarko W. Variable precision rough sets with asymmetric bounds. In: Ziarko W. (Ed). Rough Sets, Fuzzy Sets and Knowledge Discovery (1994), Springer, London 167-177
15. Klir G.J., and Yuan B. Fuzzy Sets and Fuzzy Logic: Theory and Applications (1995), Prentice-Hall, New Jersey
16. W.D. Lee, S.R. Ray, Probabilistic inference for variable certainty decisions, in: Proceedings of the 14th ACM Annual Conference on Computer Science, 1986, pp. 482.
17. Y. Li, C. Zhang, J.R. Swanb, Rough set based model in information retrieval and filtering, in: Proceedings of the 5th International Conference on Information Systems Analysis and Synthesis, 1999, pp. 398-403.
18. Li Y., Zhang C., and Swanb J.R. An information filtering model on the Web and its application in JobAgent. Knowledge-Based Systems 13 (2000) 285-296
19. In: Lin T.Y., and Cercone N. (Eds). Rough Sets and Data Mining: Analysis for Imprecise Data (1997), Kluwer Academic Publishers, Boston
20. Mi J.S., Wu W.Z., and Zhang W.X. Approaches to knowledge reduction based on variable precision rough set model. Information Sciences 159 (2004) 255-272
21. Miao D., and Hou L. A comparison of rough set methods and representative inductive learning algorithms. Fundamenta Informaticae 59 (2004) 203-219
22. Michalski R.S., and Winston P.H. Variable precision logic. Artificial Intelligence 29 (1986) 121-146
23. Mitchell T.M. Machine Learning (1997), McGraw-Hill, New York
24. Nakamura A., and Gao J.M. On a KTB-modal fuzzy logic. Fuzzy Sets and Systems 45 (1992) 327-334
25. Nguyen S.H., Skowron A., and Stepaniuk J. Granular computing: a rough set approach. Computational Intelligence 17 (2001) 514-544
26. Pawlak Z. Rough sets. International Journal of Computer and Information Sciences 11 (1982) 341-356
27. Pawlak Z. Rough Sets: Theoretical Aspects of Reasoning about Data (1991), Kluwer Academic Publishers, Boston
28. Pawlak Z., and Skowron A. Rough membership functions. In: Yager R.R., Fedrizzi M., and Kacprzyk J. (Eds). Advances in the Dempster-Shafer Theory of Evidence (1994), John Wiley and Sons, New York 251-271
29. Pawlak Z., Wong S.K.M., and Ziarko W. Rough sets: probabilistic versus deterministic approach. International Journal of Man-Machine Studies 29 (1988) 81-95
30. Polkowski L., and Skowron A. Rough mereology: a new paradigm for approximate reasoning. International Journal of Approximate Reasoning 15 (1996) 333-365
31. In: Polkowski L., and Skowron A. (Eds). Rough Sets in Knowledge Discovery 1 vols. 1-2 (1998), Physica-Verlag, Heidelberg
32. Skowron A., and Polkowski L. Rough mereology and analytical morphology. In: Orlowska E. (Ed). Incomplete Information: Rough Set Analysis (1998), Physica-Verlag, Heidelberg 399-437
33. Skowron A., and Stepaniuk J. Tolerance approximation spaces. Fundamenta Informaticae 27 (1996) 245-253
34. Ślȩzak D., sets R., and factor B. LNCS Transactions on Rough Sets III. LNCS 3400 (2005) 202-229
35. Ślȩzak D., and Ziarko W. The investigation of the Bayesian rough set model. International Journal of Approximate Reasoning 40 (2005) 81-91
36. Srinivasan P., Ruiz M.E., Kraft D.H., and Chen J. Vocabulary mining for information retrieval: rough sets and fuzzy sets. Information Processing and Management 37 (2001) 15-38
37. Stefanowski J. On rough set based approaches to induction of decision rules. In: Polkowski L., and Skowron A. (Eds). Rough Sets in Knowledge Discovery 1 (1998), Physica-Verlag, Heidelberg
38. Tsumoto S. Automated extraction of medical expert system rules from clinical databases on rough set theory. Information Sciences 112 (1998) 67-84
39. S. Tsumoto, Accuracy and coverage in rough set rule induction, in: Rough Sets and Current Trends in Computing, Proceedings of RSCTC'02, LNAI, vol. 2475, 2002, pp. 373-380.
40. van Rijsbergen C.J. Information Retrieval (1979), Butterworths, London
41. Wang G.Y. Rough reduction in algebra view and information view. International Journal of Intelligent Systems 18 (2003) 679-688
42. Wei L.L., and Zhang W.X. Probabilistic rough sets characterized by fuzzy sets. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 12 (2004) 47-60
43. Wong S.K.M., and Ziarko W. Comparison of the probabilistic approximate classification and the fuzzy set model. Fuzzy Sets and Systems 21 (1987) 357-362
44. W.Z. Wu, Upper and lower probabilities of fuzzy events induced by a fuzzy set-valued mapping, in: Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, Proceedings of RSFDGrC'05, LNAI, vol. 3641, 2005, pp. 345-353.
45. Wu W.Z., Leung Y., and Zhang W.X. On generalized rough fuzzy approximation operators, LNCS Transactions on Rough Sets V. LNCS 4100 (2006) 263-284
46. Xu Z.B., Liang J.Y., Dang C.Y., and Chin K.S. Inclusion degree: a perspective on measures for rough set data analysis. Information Sciences 141 (2002) 227-236
47. J.T. Yao, J.P. Herbert, Web-based support systems based on rough set analysis, in: Rough Sets and Emerging Intelligent Systems Paradigms, Proceedings of RSEISP'07, LNAI, vol. 4585, 2007, pp. 360-370.
48. J.T. Yao, M. Zhang, Feature selection with adjustable criteria, in: Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, Proceedings of RSFDGrC'05, LNAI, vol. 3641, 2005, pp. 204-213.
49. Yao Y.Y. Two views of the theory of rough sets in finite universes. International Journal of Approximation Reasoning 15 (1996) 291-317
50. Y.Y. Yao, On generalizing Pawlak approximation operators, in: Rough Sets and Current Trends in Computing, Proceedings of RSCTC'98, LNAI, vol. 1424, 1998, pp. 298-307.
51. Yao Y.Y. Information granulation and rough set approximation. International Journal of Intelligent Systems 16 (2001) 87-104
52. Yao Y.Y. Information granulation and approximation in a decision-theoretical model of rough sets. In: Pal S.K., Polkowski L., and Skowron A. (Eds). Rough-neural Computing: Techniques for Computing with Words (2003), Springer, Berlin 491-518
53. Y.Y. Yao, On generalizing rough set theory, in: Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, Proceedings of RSFDGrC'03, LNAI, vol. 2639, 2003, pp. 44-51.
54. Yao Y.Y. Probabilistic approaches to rough sets. Expert Systems 20 (2003) 287-297
55. Yao Y.Y. Semantics of fuzzy sets in rough set theory, LNCS Transactions on Rough Sets II. LNCS 3135 (2004) 297-318
56. Yao Y.Y., and Wong S.K.M. A decision theoretic framework for approximating concepts. International Journal of Man-machine Studies 37 (1992) 793-809
57. Yao Y.Y., Wong S.K.M., and Lin T.Y. A review of rough set models. In: Lin T.Y., and Cercone N. (Eds). Rough Sets and Data Mining: Analysis for Imprecise Data (1997), Kluwer Academic Publishers, Boston 47-75
58. Yao Y.Y., Wong S.K.M., and Lingras P. A decision-theoretic rough set model. In: Ras Z.W., Zemankova M., and Emrich M.L. (Eds). Methodologies for Intelligent Systems 5 (1990), North-Holland, New York 17-24
59. Zadeh L.A. Fuzzy sets. Information and Control 8 (1976) 338-353
60. Zhang M., Xu L.D., Zhang W.X., and Li H.Z. A rough set approach to knowledge reduction based on inclusion degree and evidence reasoning theory. Expert Systems 20 (2003) 298-304
61. W.X. Zhang, Y. Leung, Theory of including degrees and its applications to uncertainty inference, in: Soft Computing in Intelligent Systems and Information Processing, Proceedings of 1996 Asian Fuzzy System Symposium, 1996, pp. 496-501.
62. Zhang W.X., Wu W.Z., Liang J.Y., and Li D.Y. Rough Set Theory and Methodology (2001), Xi'an Jiaotong University Press, Xi'an, China (in Chinese)
63. W.Q. Zhao, Y.L. Zhu, An email classification scheme based on decision-theoretic rough set theory and analysis of email security, in: Proceedings of 2005 IEEE Region 10 TENCON, doi: 10.1109/TENCON.2005.301121.
64. Zhong N., Dong J.Z., and Ohsuga S. Data mining: a probabilistic rough set approach. In: Polkowski L., and Skowron A. (Eds). Rough Sets in Knowledge Discovery 2 (1998), Physica-Verlag, Heidelberg 127-146
65. Zhong N., and Skowron A. A rough set-based knowledge discovery process. International Journal of Mathematics and Computer Science 11 (2001) 603-619
66. Ziarko W. Variable precision rough set model. Journal of Computer and System Science 46 (1993) 39-59
67. Ziarko W. Acquisition of hierarchy-structured probabilistic decision tables and rule from data. Expert Systems 20 (2003) 305-310
68. W. Ziarko, Probabilistic rough sets, in: Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, Proceedings of RSFDGrC'05, LNAI, vol. 3641, 2005, pp. 283-293.
69. W. Ziarko, Probabilistic approach to rough sets, International Journal of Approximate Reasoning (2007), in press, doi:10.1016/j.ijar.2007.06.014.