Hostname: page-component-7dd5485656-j7khd Total loading time: 0 Render date: 2025-10-30T15:28:17.120Z Has data issue: false hasContentIssue false
  • English
  • Français

On rough sets, their recent extensions and applications

Published online by Cambridge University Press:  01 December 2010

N. Mac Parthaláin  and
Q. Shen
N. Mac Parthaláin*
Affiliation:
Department of Computer Science, Aberystwyth University, Aberystwyth, Ceredigion, SY23 3DB, Wales, UK; e-mail: ncm@aber.ac.uk, qqs@aber.ac.uk
Q. Shen*
Affiliation:
Department of Computer Science, Aberystwyth University, Aberystwyth, Ceredigion, SY23 3DB, Wales, UK; e-mail: ncm@aber.ac.uk, qqs@aber.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

Rough set theory (RST) has enjoyed an enormous amount of attention in recent years and has been applied to many real-world problems including data mining, pattern recognition, and intelligent control. Much research has recently been carried out in respect of both the development of the underlying theory and the application to new problem domains. This paper attempts to summarize the advances in RST, its extensions, and their applications. It also identifies important areas which require further investigation. Typical example application domains are examined which demonstrate the success of the application of RST to a wide variety of areas and disciplines, and which also exhibit the strengths and limitations of the respective underlying approaches.

Information

Type
Articles
Information
The Knowledge Engineering Review , Volume 25 , Issue 4 , December 2010 , pp. 365 - 395
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

American College of Radiology. 1998. Illustrated Breast Imaging Reporting and Data System BIRADS, 3rd edn. American College of Radiology.Google Scholar
Asharaf, A., Murty, M. N. 2004. An adaptive rough fuzzy single pass algorithm for clustering large data sets. Pattern Recognition 36(12), 3015–3018.CrossRefGoogle Scholar
Baldwin, J. F., Lawry, J., Martin, T. P. 1997. A mass assignment based ID3 algorithm for decision tree induction. International Journal of Intelligent Systems 12(7), 523–552.3.0.CO;2-N>CrossRefGoogle Scholar
Bao, Z., Han, B., Wu, S. 2006. A novel clustering algorithm based on variable precision rough-fuzzy sets. In Proceedings of the International Conference on Intelligent Computing (ICIC 2006). Kunming, China, August 16–19, 284–289.Google Scholar
Bazan, J., Nguyen, H. S., Nguyen, S. H., Synak, P., Wroblewski, J. 2000. Rough set algorithms in classification problem. In Rough Set Methods and Applications, Polkowski, L., Tsumoto, S. & Lin, T. Y. (eds). Physica-Verlag, 49–88.CrossRefGoogle Scholar
Bell, D. A., Guan, J. W. 1998. Computational methods for rough classification and discovery. Journal of the American Society for Information Science 5, 403–414.Google Scholar
Beynon, M. J. 2000. An investigation of β-reduct selection within the variable precision rough sets model. In Proceedings of the Second International Conference on Rough Sets and Current Trends in Computing (RSCTC 2000), Banff, Canada, 114–122.Google Scholar
Beynon, M. J. 2001. Reducts within the variable precision rough sets model: a further investigation. European Journal of Operational Research 134(3), 592–605.CrossRefGoogle Scholar
Bezdek, J. C. 1981. Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press.CrossRefGoogle Scholar
Bhatt, R. B., Gopal, M. 2004. FRID: fuzzy-rough interactive dichotomizers. In Proceeding of the 2004 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE’04), Budapest, 1337–1342.Google Scholar
Bian, H., Mazlack, L. 2003. Fuzzy-rough nearest-neighbor classification approach. In Proceeding of the 22nd International Conference of the North American Fuzzy Information Processing Society (NAFIPS), Chicago, USA, 500–505.Google Scholar
Boixader, D., Jacas, J., Recasens, J. 2000. Upper and lower approximations of fuzzy sets. International Journal of General Systems 29(4), 555–568.Google Scholar
Brassard, G., Bratley, P. 1996. Fundamentals of Algorithms. Prentice Hall.Google Scholar
Browne, C., Düntsch, I., Gediga, G. 1998. IRIS revisited, a comparison of discriminant enhanced rough set data analysis. In Rough Sets in Knowledge Discovery 2: Applications, Case Studies and Software Systems, Polkowski, L & Skowron, A. (eds). Physica-Verlag, 347–370.Google Scholar
Chen, D., Zhang, W. X., Yeung, D., Tsang, E. C. C. 2006. Rough approximations on a complete completely distributive lattice with applications to generalized rough sets. Information Sciences 176(13), 1829–1848.Google Scholar
Chimphlee, S., Salim, N., Ngadiman, M. S. B., Chimphlee, W., Srinoy, S. 2006. Independent component analysis and rough fuzzy based approach to web usage mining. In Proceedings of the 24th IASTED International Conference on Artificial Intelligence and Applications, Deved, V, (ed.). International Association of Science and Technology for Development, 422–427. ACTA Press.Google Scholar
Chimphlee, W., Abdullah, A. H., Sap, M. N. M., Srinoy, S., Chimphlee, S. 2006a. Anomaly-based intrusion detection using fuzzy rough clustering. International Conference on Hybrid Information Technology (ICHIT’06) 1, 329–334.Google Scholar
Chouchoulas, A., Shen, Q. 2001. Rough set-aided keyword reduction for text categorisation. Applied Artificial Intelligence 15(9), 843–873.CrossRefGoogle Scholar
Cordon, O., Gomide, F., Herrera, F., Hoffmann, F., Magdalena, L. 2001. Ten years of genetic fuzzy systems: current framework and new trends. Fuzzy Sets and Systems 141, 5–31.CrossRefGoogle Scholar
Cornelis, C., De Cock, M., Radzikowska, A. 2007. Vaguely quantified rough sets. In Proceedings of the 11th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing (RSFDGrC2007), Lecture Notes in Artificial Intelligence 4482, 87–94.Google Scholar
Cornelis, C., Jensen, R. 2008. A noise-tolerant approach to fuzzy-rough feature selection. In Proceedings of the 17th International Conference on Fuzzy Systems (FUZZ-IEEE’08), Hong Kong, China, 1598–1605.Google Scholar
Dash, M., Liu, H. 1997. Feature selection for classification. Intelligent Data Analysis 1(3), 131–156.Google Scholar
Davis, M., Logemann, G., Loveland, D. 1962. A machine program for theorem proving. Communications of the ACM 5, 394–397.CrossRefGoogle Scholar
De Cock, M., Cornelis, C., Kerre, E. E. 2004. Fuzzy rough sets: beyond the obvious. IEEE International Conference on Fuzzy Systems 1, 103–108.Google Scholar
Deogun, J. S., Raghavan, V. V., Sever, H. 1994. Rough set based classification methods and extended decision tables. In Proceedings of the International Workshop on Rough Sets and Soft Computing. San Jose, California, 302–309.Google Scholar
Deogun, J. S., Raghavan, V. V., Sever, H. 1995. Exploiting upper approximations in the rough set methodology. In Proceedings of the First International Conference on Knowledge Discovery and Data Mining. Quebec, Canada, 1–10.Google Scholar
Devijver, P., Kittler, J. 1982. Pattern Recognition: A Statistical Approach. Prentice Hall.Google Scholar
Dubois, D., Prade, H. 1990. Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems 17, 191–209.CrossRefGoogle Scholar
Dubois, D., Prade, H. 1992. Putting rough sets and fuzzy sets together. In Intelligent Decision Support: Handbook of Applications and Advances of the Sets Theory, Slowinski, R. (ed.). Kluwer, 203–232.Google Scholar
Dunn, J. C. 1973. A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters. Journal of Cybernetics 3, 32–57.Google Scholar
Glymin, M., Ziarko, W. 2007. Rough set approach to spam filter learning. In Proceedings of Rough Sets and Emerging Intelligent Systems Paradigms (RSEISP’07), Lecture Notes in Artificial Intelligence 4585, 350–359.Google Scholar
Greco, S., Matarazzo, B., Slowiński, R. 2001. Rough sets theory for multicriteria decision analysis. European Journal of Operational Research 129(1), 1–47.Google Scholar
Grzymala-Busse, D. M., Grzymala-Busse, J. W. 1995. The usefulness of machine learning approach to knowledge acquisition. Computational Intelligence 11, 268–279.Google Scholar
Grzymala-Busse, J. W., Wang, C. P. B. 1996. Classification methods in rule induction. In Proceedings of the 5th Intelligent Information Systems Workshop, Dęblin, Poland, 120–126.Google Scholar
Grzymala-Busse, J. W. 2003. A comparison of three strategies to rule induction from data with numerical attributes. In Proceedings of the International Workshop on Rough Sets in Knowledge Discovery (RSKD 2003), Warsaw, Poland, 132–140.Google Scholar
Grzymala-Busse, J. W. 2006. Rough set theory with applications to data mining. In Real World Applications of Computational Intelligence, Studies in Fuzziness and Soft Computing Series, Negoita, M. & Reusch, B. (eds). Springer, Heidelberg, 223–244.Google Scholar
Han, J., Hu, X., Lin, T. Y. 2005. Feature subset selection based on relative dependency between Attributes. In Rough Sets and Current Trends in Computing: 4th International Conference (RSCTC 2004). Uppsala, Sweden, June 1–5, 176–185.Google Scholar
Heath, M., Bowyer, K., Kopans, D., Moore, R., Kegelmeyer, P. J. 2000. The digital database for screening mammography. In Proceedings of the International Workshop on Digital Mammography, Madison, Wiscowsow, USA, 212–218.Google Scholar
Hirano, S., Tsumoto, S. 2000. Rough clustering and its application to medicine. Journal of Information Sciences 124, 125–137.Google Scholar
Hirano, S., Tsumoto, S. 2003. Indiscernibility-based clustering: rough clustering. In International Fuzzy Systems Association World Congress, Lecture Notes in Computer Science 2715, 378–386. Springer-Verlag.Google Scholar
Ho, B., Nguyen, N. B. 2002. Nonhierarchical document clustering based on a tolerance rough set model. International Journal of Intelligent Systems 17(2), 199–212.Google Scholar
Ho, T. B., Kawasaki, S., Nguyen, N. B. 2006. Documents clustering using tolerance rough set model and its application to information retrieval. In Studies In Fuzziness and Soft Computing, Intelligent Exploration of the Web, Szczepaniak, P.S., Segovia, J., Karprzyk, J., & Zadeh, L.A. (eds). Physica-Verlag, Heidelberg, 181–196.Google Scholar
Hong, T. P., Liou, Y. L., Wang, S. L. 2006. Learning with hierarchical quantitative attributes by fuzzy rough sets. In Proceedings of the 2006 Joint Conference on Information Sciences, Advances in Intelligent Systems Research, Taiwan, ROC, 1309–1312.Google Scholar
Hu, Q.-H., Yu, D.-R. 2004. Variable precision dominance based rough set model and reduction algorithm for preference-ordered data. Proceedings of the 2004 International Conference on Machine Learning and Cybernetics 4, 2279–2284.Google Scholar
Hu, Q.-H., Yu, D.-R. 2005. Fuzzy rough C-means clustering. In World Congress on Fuzzy Logic, Soft Computing, Computational Intelligence: Theories and Applications (IFSA2005), Springer Lecture Notes, Tsinghua, Beijing.Google Scholar
Hu, Q., Yu, D., Xie, Z. 2006. Information-preserving hybrid data reduction based on fuzzy-rough techniques. Pattern Recognition Letters 27(5), 414–423.CrossRefGoogle Scholar
Hu, Q., Zhao, H., Xie, Z., Yu, D. 2007a. Consistency based attribute reduction. In Proceedings of the Pacific-Asia Conference on Knowledge Discovery and Data Mining 2007, Zhou, Z., Li, H. & Yang, Q. (eds). Lecture Notes in Computer Science 4426, 96–107.Google Scholar
Hu, Q., Xie, Z., Yu, D. 2007b. Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation. Pattern Recognition 40, 3509–3521.Google Scholar
Inuiguchi, M., Tsurumi, M. 2006. Measures based on upper approximations of rough sets for analysis of attribute importance and interaction. International Journal of Innovative Computing Information and Control 2(1), 1–12.Google Scholar
Jelonek, J., Krawiec, K., Slowiński, R., Stefanowski, J., Szymas, J. 1994. Rough sets as an intelligent front-end for the neural network. In Proceedings of the First National Conference on Neural Networks Their Applications 2, Poland, 116–122.Google Scholar
Jensen, R., Shen, Q. 2004a. Semantics-preserving dimensionality reduction: rough and fuzzy-rough based approaches. IEEE Transactions on Knowledge and Data Engineering 16(12), 1457–1471.CrossRefGoogle Scholar
Jensen, R., Shen, Q. 2004b. Fuzzy-rough attribute reduction with application to web categorization. Fuzzy Sets and Systems 141(3), 469–485.CrossRefGoogle Scholar
Jensen, R., Shen, Q. 2005. Fuzzy-rough data reduction with ant colony optimization. Fuzzy Sets and Systems 149(1), 5–20.CrossRefGoogle Scholar
Jensen, R., Shen, Q. 2007. Fuzzy-rough sets assisted attribute selection. IEEE Transactions on Fuzzy Systems 15(1), 73–89.CrossRefGoogle Scholar
Jensen, R., Cornelis, C. 2008. A new approach to fuzzy-rough nearest neighbour classification. In Proceedings of the 6th International Conference on Rough Sets and Current Trends in Computing, Akron, Ohio, USA, 310–319.Google Scholar
Jensen, R., Shen, Q. 2008. Computational Intelligence and Feature Selection: Rough and Fuzzy Approaches. IEEE Press and Wiley & Sons.CrossRefGoogle Scholar
Jensen, R., Shen, Q. 2009. New approaches to fuzzy-rough feature selection. IEEE Transactions on Fuzzy Systems 17(4), 824–838.Google Scholar
Jian, L.-R., Li, M.-Y. 2007. An extension of VPRS model based on dominance relation. Proceedings of the 4th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2007) 3, 113–118.CrossRefGoogle Scholar
Kawasaki, S., Nguyen, N. B., Ho, T. B. 2000. Hierarchical document clustering based on tolerance rough set model. In Principles of Data Mining and Knowledge Discovery, 4th European Conference (PKDD 2000), Lyon, France (September 13–16, 2000), Zighed, D. A., Komorowski, H. J. & Zytkow, J. M. (eds). Lecture Notes in Computer Science 1910, 13–27. Springer.Google Scholar
Ke, L., Feng, Z., Ren, Z. 2008. An efficient ant colony optimization approach to attribute reduction in rough set theory. Pattern Recognition Letters 29, 1351–1357.CrossRefGoogle Scholar
Keller, J. M., Gray, M. R., Givens, J. A. 1985. A fuzzy K-nearest neighbor algorithm. IEEE Transactions on Systems Man and Cybernetics 15(4), 580–585.Google Scholar
Kim, D., Bang, S.-Y. 2000. A handwritten numeral character classification using tolerant rough set. IEEE Transactions on Pattern Analysis and Machine Intelligence 22(9), 923–937.Google Scholar
Komorowski, J., Pawlak, Z., Polkowski, L., Skowron, A. 1999. Rough sets: a tutorial. In Rough-Fuzzy Hybridization: A New Trend in Decision Making, Pal, S. K. & Skowron, A. (eds). Springer-Verlag, 3–98.Google Scholar
Kotłowski, W., Dembczyński, K., Greco, S., Słowiński, R. 2008. Stochastic dominance-based rough set model for ordinal classification. International Journal of Information Sciences 178(21), 4019–4037.CrossRefGoogle Scholar
Kryszkiewicz, M. 1994. Maintenance of Reducts in the Variable Precision Rough Sets Model. ICS Research Report 31/94, Warsaw University of Technology.Google Scholar
Kumar, P., Krishna, P. R., Bapi, R. S., De, S. K. 2007. Rough clustering of sequential data. Data & Knowledge Engineering 63(2), 183–199.Google Scholar
Li, R., Wang, Z.-O. 2004. Mining classification rules using rough sets and neural networks. European Journal of Operational Research 157, 439–448.Google Scholar
Li, M., Wu, C., Zhang, Y., Yue, Y. 2006. An improved BP network classifier based on VPRS feature reduction. The Sixth World Congress on Intelligent Control and Automation (WCICA 2006) 2, 9677–9680.Google Scholar
Lingras, P. 1996. Rough neural networks. Proceedings of the Sixth International Conference on Information Processing Management of Uncertainty in Knowledge-based Systems (IPMU’96) 2, 1445–1450.Google Scholar
Lingras, P. 1997. Comparison of neofuzzy rough neural networks. In Proceedings of the Fifth International Workshop on Rough Sets Soft Computing (RSSC’97), 259–262.Google Scholar
Lingras, P., Davies, C. 2001. Applications of rough genetic algorithms. Computational Intelligence 17(3), 435–445.CrossRefGoogle Scholar
Lingras, P., West, C. 2004. Interval set clustering of web users with rough K-means. Journal of Intelligent Information Systems 23(1), 5–16.CrossRefGoogle Scholar
Lingras, P., Hogo, M., Snorek, M. 2004. Interval set clustering of web users using modified Kohonen self-organizing maps based on the properties of rough sets. Web Intelligence and Agent Systems 2(3), 217–230.Google Scholar
Mak, B., Munakata, T. 2002. Rule extraction from expert heuristics: a comparative study of rough sets with neural networks and ID3. European Journal of Operational Research 136, 212–229.CrossRefGoogle Scholar
Malyszko, D., Stepaniuk, J. 2008. Standard and fuzzy rough entropy clustering algorithms in image segmentation. Rough Sets and Current Trends in Computing 5306, 409–418.Google Scholar
Mac Parthaláin, N., Shen, Q., Jensen, R. 2010. A distance measure approach to exploring the rough set boundary region for attribute reduction. IEEE Transactions on Knowledge and Data Engineering 22(3), 306–317.Google Scholar
Mac Parthaláin, N., Jensen, R., Shen, Q., Zwiggelaar, R. 2010. Rough and fuzzy-rough methods for mammographic data analysis. Intelligent Data Analysis—An International Journal 14(2), 225–244.CrossRefGoogle Scholar
Mac Parthaláin, N., Shen, Q. 2009. Exploring the boundary region of tolerance rough sets for feature selection. Pattern Recognition 42(5), 655–667.CrossRefGoogle Scholar
McKee, T., Lensberg, T. 2002. Genetic programming and rough sets: a hybrid approach to bankruptcy classification. European Journal of Operational Research 140(2), 436–451.Google Scholar
Mi, J. S., Zhang, W. X. 2004. An axiomatic characterization of a fuzzy generalization of rough sets. Information Sciences 160(1–4), 235–249.CrossRefGoogle Scholar
Mieszkowicz-Rolka, A., Rolka, L. 2004. Fuzzy implication operators in variable precision fuzzy rough sets model. Lecture Notes in Computer Science (LNCS) 3070, Springer, Heidelberg, 498–503.Google Scholar
Mitra, S., Banerjee, M. 1996. Knowledge based neural net with rough sets. In Methodologies for the Conception, Design, Application of Intelligent Systems, Proceedings of the Fourth International Conference on Soft Computing (IIZUKA’96), Yamakawa, T. & Matsumoto, G. (eds). World Scientific, 213–216.Google Scholar
Mitra, P., Mitra, S. 2000. Staging of cervical cancer with soft computing. IEEE Transactions on Biomedical Engineering 47(7), 934–940.CrossRefGoogle ScholarPubMed
Modrzejewski, M. 1993. Feature selection using rough sets theory. In Proceedings of the 11th International Conference on Machine Learning, New Brunswick, NJ, USA, 213–226.Google Scholar
Molina, L. C., Belanche, L., Nebot, A. 2002. Feature selection algorithms: a survey and experimental evaluation. In Proceedings of ICDM02, Maebashi City, Japan, 306–313.Google Scholar
Momin, B. F., Mitra, S., Gupta, R. D. 2006. Reduct generation and classification of gene expression data. Proceedings of the 2006 International Conference on Hybrid information Technology (ICHIT06) 1, 699–708.Google Scholar
Morsi, N. N., Yakout, M. M. 1998. Axiomatics for fuzzy rough sets. Fuzzy Sets and Systems 100(1–3), 327–342.CrossRefGoogle Scholar
Narendra, P., Fukunaga, K. 1977. A branch and bound algorithm for feature subset selection. IEEE Transactions on Computers C-26(9), 917–922.Google Scholar
Ngo, C. L., Nguyen, H. S. 2004. A tolerance rough set approach to clustering web search results. In Proceedings of the 8th European Conference on Principles and Practice of Knowledge Discovery in Databases (Pisa, Italy, September 20–24, 2004), Boulicaut, J., Esposito, F., Giannotti, F. & Pedreschi, D. (eds). Lecture Notes in Computer Science 3202, Springer-Verlag New York, New York, 515–517.Google Scholar
Nguyen, S. H., Skowron, A. 1997a. Searching for relational patterns in data. In Proceedings of the First European Symposium on Principles of Data Mining and Knowledge Discovery, Trondheim, Norway, 265–276.Google Scholar
Nguyen, S. H., Slezak, D. 2004. Approximate reducts and association rules correspondence and complexity results. Lecture Notes in Computer Science (LNCS), Zhong, N., Skowron, A., & Ohsuga, S. (eds). 1711, Springer, Heidelberg, 137–145.Google Scholar
Øhrn, A. 1999. Discernibility and Rough Sets in Medicine: Tools and Applications. Department of Computer and Information Science, Norwegian University of Science and Technology, Trondheim, Norway, 239.Google Scholar
Oliver, A., Freixenet, J., Marti, R., Pont, J., Perez, E., Denton, E. R. E., Zwiggelaar, R. 2008. A novel breast tissue density classification methodology. IEEE Transactions on Information Technology in Biomedicine 12(1), 55–65.Google Scholar
Pal, S. K. 2004. Pattern Recognition Algorithms for Data Mining. Chapman and Hall.Google Scholar
Pattaraintakorn, P., Cercone, N. 2007. Integrating rough set theory and medical applications. Applied Mathematics Letters 21(4), 400–403.Google Scholar
Pawlak, Z. 1982. Rough sets. International Journal of Computing and Information Sciences 11, 341–356.CrossRefGoogle Scholar
Pawlak, Z. 1984. Rough classification. International Journal of Man-Machine Studies 20, 469–483.CrossRefGoogle Scholar
Pawlak, Z., Slowinski, K., Slowinski, R. 1986. Rough classification of patients after highly selective vagotomy for duodenal ulcer. International Journal of Man Machine Studies 24, 413–433.Google Scholar
Pawlak, Z. 1991. Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishing.Google Scholar
Pawlak, Z., Skowron, A. 1993. A rough set approach for decision rules generation. ICS Research Report 23/93, Warsaw University of Technology. Proceedings of the International Joint Conference on Artificial Intelligence ’93 Workshop W12: The Management of Uncertainty in AI, France.Google Scholar
Pawlak, Z. 2003. Some issues on rough sets. Lecture Notes on Computer Science, Transactions on Rough Sets 1, Springer, Heidelberg, 1–53.Google Scholar
Pedrycz, W. 1999. Shadowed sets: bridging fuzzy and rough sets. In Rough-Fuzzy Hyridisation, Pal, S. K. & Skowron, A. (eds). Springer-Verlag, 179–199.Google Scholar
Peters, J. F., Skowron, A., Suraj, Z., Rzasa, W., Bokowski, M. 2002. Clustering: a rough set approach to constructing information granules. In Proceedings of the 6th International Conference on Soft Computing and Distributed Processing, Rzeszow, Poland, 57–61.Google Scholar
Petrosino, A., Ceccarelli, M. 2000. Unsupervised texture discrimination based on rough fuzzy sets and parallel hierarchical clustering. In Proceedings of the International Conference on Pattern Recognition (ICPR ’00) 3 (September 03–08, 2000), IEEE Computer Society, Washington, DC.Google Scholar
Polkowski, L., Skowron, A. 1998. Rough sets: a perspective. In Rough Sets in Knowledge Discovery 1: Methodology and Applications, Polkowski, L. & Skowron, A. (eds). Physica-Verlag, 31–56.Google Scholar
Qina, K., Pei, Z. 2005. On the topological properties of fuzzy rough sets. Fuzzy Sets and Systems 151(3), 601–613.Google Scholar
Radzikowska, A. M., Kerre, E. E. 2002. A comparative study of fuzzy rough sets. Fuzzy Sets and Systems 126(2), 137–155. Elsevier, Amsterdam.Google Scholar
Radzikowska, A. M., Kerre, E. E. 2004. Fuzzy rough sets based on residuated lattices. Transactions on Rough Sets II, Lecture Notes in Computer Science (LNCS) 3135, 278–296.Google Scholar
Sarkar, M. 2000. Fuzzy-rough nearest neighbors algorithm. In Proceedings of the IEEE Conference on Systems Man and Cybernetics, Nashville, TN, USA, 3556–3561.Google Scholar
Sarkar, M. 2007. Fuzzy-rough nearest neighbors algorithm. Fuzzy Sets and Systems 158, 2123–2152.Google Scholar
Shafer, G. 1976. A Mathematical Theory of Evidence. Princeton University Press.Google Scholar
Shan, D., Ishii, N., Hujun, Y., Allinson, N., Freeman, R., Keane, J., Hubbard, S. 2002. Feature weights determining of pattern classification by using a rough genetic algorithm with fuzzy similarity measure. In Proceedings of Intelligent Data Engineering and Automated Learning, Manchester, UK, 544–550.Google Scholar
Shang, C., Shen, Q. 2002. Rough feature selection for neural network based image classification. International Journal of Image and Graphics 2(4), 541–555.Google Scholar
Shao, M.-W., Zhang, W.-X. 2004. Dominance relation and rules in an incomplete ordered information system. International Journal of Intelligent Systems 20(1), 13–20.Google Scholar
Shen, Q., Chouchoulas, A. 2000. A modular approach to generating fuzzy rules with reduced attributes for the monitoring of complex systems. Engineering Applications of Artificial Intelligence 13(3), 263–278.CrossRefGoogle Scholar
Shen, Q., Chouchoulas, A. 2002. A rough-fuzzy approach for generating classification rules. Pattern Recognition 35(2), 2425–2438.Google Scholar
Shen, Q., Jensen, R. 2004. Selecting informative features with fuzzy-rough sets and its application for complex systems monitoring. Pattern Recognition 37(7), 1351–1363.Google Scholar
Skowron, A., Rauszer, C. 1992. The discernibility matrices and functions in information systems. In Intelligent Decision Support: Handbook of Applications and Advances to Rough Sets Theory, Slowinski, R. (ed.). Kluwer Academic, 331–362.Google Scholar
Skowron, A. 1993. Boolean reasoning for decision rules generation. In Proceedings of the 7th International Symposium ISMIS’93, Komorowski, J. & Ras, Z. (eds). Lecture Notes in Artificial Intelligence, Trondheim, Norway 689, 295–305. Springer-Verlag.Google Scholar
Skowron, A., Stepaniuk, J. 1994. Generalized approximation spaces. In Proceedings of the 3rd International Workshop on Rough Sets and Soft Computing, San Jose, California, USA, 156–163.Google Scholar
Skowron, A., Stepaniuk, J. 1996. Tolerance approximation spaces. Fundamenta Informaticae 27, 245–253.Google Scholar
Skowron, A., Pawlak, Z., Komorowski, J., Polkowski, L. 2002. A rough set perspective on data and knowledge. In Handbook of Data Mining and Knowledge Discovery, Kloesgen, W., & Zytkow, J. (eds). Oxford University Press, 134–149.Google Scholar
Slowinski, R., Vanderpooten, D. 1997. Similarity relations as a basis for rough approximations. In Advances in Machine Intelligence and Soft Computing, Wang, P. P. (ed.). Bookwrights, 17–33.Google Scholar
Slowinski, R., Vanderpooten, D. 2000. A generalized definition of rough approximations based on similarity. IEEE Transactions on Knowledge and Data Engineering 12(2), 331–336.Google Scholar
Slowinski, K., Stefanowski, J., Siwinski, D. 2002. Application of rule induction and rough sets to verification of magnetic resonance diagnosis. Fundamenta Informaticae 53(3/4), 345–363.Google Scholar
Srinivasan, P., Ruiz, M. E., Kraft, D. H., Chen, J. 1998. Vocabulary mining for information retrieval: rough sets and fuzzy sets. Information Processing & Management 37(1), 15–38.Google Scholar
Stefanowski, J. 1998. On rough set based approaches to induction of decision rules. In Rough Sets in Knowledge Discovery, Skowron, A. & Polkowski, L. (eds). 1, Physica-Verlag, 500–529.Google Scholar
Suckling, J., Partner, J., Dance, D. R., Astley, S. M., Hutt, I., Boggis, C. R. M., Ricketts, I., Stamatakis, E., Cerneaz, N., Kok, S. L., Taylor, Betal, P., Savage, J. 1994. The mammographic image analysis society digital mammogram database. In International Workshop on Digital Mammography, York, UK, 211–221.Google Scholar
Swiniarski, R., Hunt, F., Chalvet, D., Pearson, D. 1995. Intelligent data processing and dynamic process discovery using rough sets, statistical reasoning and neural networks in a highly automated production system. In Proceedings of the First European Conference on Application of Neural Networks in Industry, Helsinki, Finland.Google Scholar
Swiniarski, R. 1998. Rough sets Bayesian methods applied to cancer detection. In Proceeding of the First International Conference on Rough Sets and Soft Computing (RSCTC’98), Polkowski, L. & Skowron, A. (eds). LNAI 1424, 609–616. Springer-Verlag, 275–300.Google Scholar
Swiniarski, R. 1999. Rough sets and principal component analysis and their applications in data model building and classification. In Rough Fuzzy Hybridization: New Trends in Decision Making, Pal, S. K. & Skowron, A. (eds). Springer-Verlag, 275–300.Google Scholar
Swiniarski, R., Skowron, A. 2003. Rough set methods in feature selection and recognition. Pattern Recognition Letters 24(6), 83–849.Google Scholar
Thangavel, K., Pethalakshmi, A., Jaganathan, P. 2006. A comparative analysis of feature selection algorithms based on rough set theory. International Journal of Soft Computing 1(4), 288–294.Google Scholar
Thiele, H. 1998. Fuzzy Rough Sets Versus Rough Fuzzy Sets – An Interpretation and a Comparative Study Using Concepts of Modal Logics. Technical report no. CI-30/98, University of Dortmund.Google Scholar
Tsang, E. C. C., Chen, D., Yeung, D. S., Wang, X.-Z., Lee, J. 2008. Attributes reduction using fuzzy rough sets. IEEE Transactions on Fuzzy Systems 16(5), 1130–1141.Google Scholar
Wang, J., Wang, J. 2001. Reduction algorithms based on discernibility matrix: the ordered attributes method. Journal of Computer Science & Technology 16(6), 489–504.Google Scholar
Wang, Y., Ding, M., Zhou, C., Zhang, T. 2005. A hybrid method for relevance feedback in image retrieval using rough sets and neural networks. International Journal of Computational Cognition 3(1), 78–87.Google Scholar
Wang, X., Yang, J., Teng, X., Peng, N. 2005a. Fuzzy-rough set based nearest neighbor clustering classification algorithm. Lecture Notes in Computer Science 3613, 370–373.CrossRefGoogle Scholar
Wang, Z., Shao, X., Zhang, G., Zhu, H. 2005b. Integration of variable precision rough set and fuzzy clustering: an application to knowledge acquisition for manufacturing process planning. In Proceedings of the 10th Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing (RSFDGrC 2005), Regina, Canada.Google Scholar
Wang, X., Yang, J., Teng, X., Xia, W., Jensen, R. 2007. Feature selection based on rough sets and particle swarm optimization. Pattern Recognition Letters 28(4), 459–471.Google Scholar
Wojdyllo, P. 1998. Wavelets, rough sets arificial neural networks in EEG analysis. In Proceedings of the First International Conference on Rough Sets and Soft Computing (RSCTC’98), Polkowski, L. & Skowron, A. (eds). LNAI 1424, 444–449. Springer-Verlag.Google Scholar
Wróblewski, J. 1995. Finding minimal reducts using genetic algorithms. In Proceedings of the International Workshop on Rough Sets Soft Computing at Second Annual Joint Conference on Information Sciences (JCIS’95), Wrightsville Beach, NC, USA, 186–189.Google Scholar
Wu, W. Z., Mi, J. S., Zhang, W. X. 2003. Generalized fuzzy rough sets. Information Sciences 151, 263–282.Google Scholar
Wu, W. Z., Zhang, W. X. 2004. Constructive and axiomatic approaches of fuzzy approximation operators. Information Sciences 159(3–4), 233–254.Google Scholar
Wu, W. Z. 2005. A study on relationship between fuzzy rough approximation operators and fuzzy topological spaces. In Fuzzy Systems and Knowledge Discovery 2005, Wang, L. & Jin, Y. (eds). Lecture Notes in Artficial Intelligence 3613, 167–174. Springer, Heidelberg.Google Scholar
Wu, W. Z., Leung, Y., Mi, J. S. 2005. On characterizations of (I,T)-fuzzy rough approximation operators. Fuzzy Sets and Systems 154(1), 76–102.Google Scholar
Wygralak, M. 1989. Rough sets and fuzzy sets – some remarks on interrelations. Fuzzy Sets and Systems 29(2), 241–243.Google Scholar
Yahia, M., Mahmod, R., Sulaiman, N., Ahmad, F. 2000. Rough neural expert systems. Expert Systems with Applications 27(2), 87–99.Google Scholar
Yao, Y. Y. 1997. Combination of rough and fuzzy sets based on α-level sets. In Rough Sets and Data Mining: Analysis of Imprecise Data, Lin, T. Y. & Cereone, N. (eds). Kluwer Academic Publishers, 301–321.Google Scholar
Yeung, D. S., Chen, D., Tsang, E. C. C., Lee, J. W. T., Xizhao, W. 2005. On the generalization of fuzzy rough sets. IEEE Transactions on Fuzzy Systems 13(3), 343–361.Google Scholar
Yi, G., Hu, H., Lu, Z. 2005. Web document classification based on extended rough set. In Proceedings of the Sixth International Conference on Parallel and Distributed Computing Applications and Technology (PDCAT), IEEE Computer Society, Washington, DC, 916–919.Google Scholar
Yun, O., Ma, J. 2006. Land cover classification based on tolerant rough set. International Journal of Remote Sensing 27(14), 3041–3047.Google Scholar
Zadeh, L. A. 1965. Fuzzy sets. Information and Control 8(3), 338–353.Google Scholar
Zhao, Y., Zhang, H., Pan, Q. 2003. Classification using the variable precision rough set. In Proceedings of Rough Sets, Fuzzy Sets, Data Mining and Granular Computing 2003 2639, 350–353. Chongqing.Google Scholar
Zhao, S., Zhang, Z. 2005. A generalized definition of rough approximation based on similarity in variable precision rough sets. In Proceedings of the 2005 International Conference on Machine Learning and Cybernetics, Guangzhou, China, 3153–3156.Google Scholar
Zhao, Y., Zhou, X., Tang, G. 2005. A rough set-based fuzzy clustering. In Proceedings of the Second Asia Information Retrieval Symposium, Jeju Island, Korea, 401–409.Google Scholar
Zhao, W. Q., Zhu, Y. L. 2006. Classifying email using variable precision rough set approach. Lecture Notes in Artificial Intelligence 4062, 766–771.Google Scholar
Zheng, X., Wang, J. 2008. Power transformer fault diagnosis based on variable precision rough set. In Proceedings of the 3rd International Conference on Electric Utility Deregulation and Restructuring and Power Technologies, Nanjing, China, 1353–1358.Google Scholar
Zhong, N., Dong, J., Ohsuga, S. 2001. Using rough sets with heuristics for feature selection. Journal of Intelligent Information Systems 16(3), 199–214.Google Scholar
Ziarko, W. 1993. Variable precision rough set model. Journal of Computer and Systems Sciences 46(1), 39–59.Google Scholar
Ziarko, W. 2003. Acquisition of hierarchy-structured probabilistic decision tables and rules from data. Expert Systems 20(5), 305–310.Google Scholar