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Rough sets, their extensions and applications

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Abstract

Rough set theory provides a useful mathematical foundation for developing automated computational systems that can help understand and make use of imperfect knowledge. Despite its recency, the theory and its extensions have been widely applied to many problems, including decision analysis, data mining, intelligent control and pattern recognition. This paper presents an outline of the basic concepts of rough sets and their major extensions, covering variable precision, tolerance and fuzzy rough sets. It also shows the diversity of successful applications these theories have entailed, ranging from financial and business, through biological and medicine, to physical, art, and meteorological.

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References

  1. Z. Pawlak. Rough Sets. International Journal of Computer and Information Sciences, no. 11, pp. 341–356, 1982.

  2. Z. Pawlak. Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishing, Dordrecht, 1991.

    MATH  Google Scholar 

  3. Z. Pawlak. Some Issues on Rough Sets. Transactions on Rough Sets, vol. 1, pp. 1–58, 2004.

    MathSciNet  Google Scholar 

  4. I. Düntsch, G. Gediga. Rough Set Data Analysis. Encyclopedia of Computer Science and Technology, vol. 43, no. 28, pp. 281–301, 2000.

    Google Scholar 

  5. S. Hayri, V. V. Raghavan, T. D. Johnsten. The Status of Research on Rough Sets for Knowledge Discovery in Databases. In: Proceedings of the Second International Conference on Nonlinear Problems in Aviation and Aerospace, Daytona Beach, Florida, USA, vol. 2, pp. 673–680, 1998.

    Google Scholar 

  6. A. Skowron, Z. Pawlak, J. Komorowski, L. Polkowski. A Rough Set Perspective on Data and Knowledge. Handbook of Data Mining and Knowledge Discovery, Oxford University Press, pp. 134–149, 2002.

  7. S. K. Pal, A. Skowron. Pattern Recognition Letters-Special Issue on Rough Sets, Pattern Recognition and Data Mining, vol. 24, no. 6, pp. 829–933, 2003.

    Google Scholar 

  8. A. Skowron, J. W. Grzymala-Busse. From Rough Set Theory to Evidence Theory. In Advances in the Dempster-Shafer Theory of Evidence, R. Yager, M. Fedrizzi, and J. Kasprzyk (eds.), John Wiley & Sons Inc., New York, 1994.

    Google Scholar 

  9. Z. Pawlak, A. Skowron. Rough Membership Functions. In Advances in the Dempster-Shafer Theory of Evidence, R. Yager, M. Fedrizzi, J. Kacprzyk (eds.), Wiley, New York, pp. 251–271, 1994.

    Google Scholar 

  10. M. Wygralak. Rough Sets and Fuzzy Sets — Some Remarks on Interrelations. Fuzzy Sets and Systems, vol. 29, no. 2, pp. 241–243, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  11. A. P. Dempster. A Generalization of Bayesian Inference. Journal of the Royal Statistical Society, Series B, vol. 30, no. 2, pp. 205–247, 1968.

    MathSciNet  Google Scholar 

  12. G. Shafer. A Mathematical Theory of Evidence, Princeton University Press, 1976.

  13. L.A. Zadeh. Fuzzy Sets. Information and Control, vol. 8, no.3, pp. 338–353, 1965.

    Article  MATH  MathSciNet  Google Scholar 

  14. M. Dash, H. Liu. Feature Selection for Classification. Intelligent Data Analysis, vol. 1, no. 3, pp. 131–156, 1997.

    Article  Google Scholar 

  15. J. J. Alpigini, J. F. Peters, A. Skowron, N. Zhong, (eds). Rough Sets and Current Trends in Computing, Springer, 2002.

  16. R. W. Swiniarski, A. Skowron. Rough Set Methods in Feature Selection and Recognition. Pattern Recognition Letters, vol. 24, no. 6, pp. 833–849, 2003.

    Article  MATH  Google Scholar 

  17. A. Chouchoulas, Q. Shen. Rough Set-aided Keyword Reduction for Text Categorisation. Applied Artificial Intelligence, vol. 15, no. 9, pp. 843–873, 2001.

    Article  Google Scholar 

  18. L. Polkowski, S. Tsumoto, T. Y. Lin, (eds). Set Methods and Applications: New Developments in Knowledge Discovery in Information Systems (Studies in Fuzziness and Soft Computing), Physica-Verlag, Heidelberg, vol. 56, 2000.

    Google Scholar 

  19. L. Polkowski. Rough Sets: Mathematical Foundations, Physica-Verlag, Heidelberg, 2002.

    MATH  Google Scholar 

  20. J. Komorowski, Z. Pawlak, L. Polkowski, A. Skowron. Rough Sets: A Tutorial. In Rough-Fuzzy Hybridization: A New Trend in Decision Making, Springer-Verlag Singapore Ltd, pp. 3–98, 1999.

  21. A. Skowron, C. Rauszer. The Discernibility Matrices and Functions in Information Systems. In Intelligent Decision Support-handbook of Applications and Advances of the Rought Set Theory, Kluwer Academic Publisher, Dordrecht, pp. 331–362, 1992.

    Google Scholar 

  22. W. W. Koczkodaj, M. Orlowski, V. W. Marek. Myths about Rough Set Theory. Communications of the ACM, vol. 41, no. 11, pp. 102–103, 1998.

    Article  Google Scholar 

  23. W. Ziarko. Variable Precision Rough Set Model. Journal of Computer and System Sciences, vol. 46, no. 1, pp. 39–59, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  24. D. Dubois, H. Prade. Putting Rough Sets and Fuzzy Sets Together. Intelligent Decision Support: Handbook of Applications and Advances of the Rough Set Theory, Kluwer Academic Publishers, Dordrecht, pp. 203–232, 1992.

    Google Scholar 

  25. A. Skowron, J. Stepaniuk. Tolerance Approximation Spaces. Fundamenta Informaticae, vol. 27, no. 2–3, pp. 245–253, 1996.

    MATH  MathSciNet  Google Scholar 

  26. M. J. Beynon. 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, pp 114–122, 2000.

  27. M. Beynon. Reducts within the Variable Precision Rough Sets Model: A Further Investigation. European Journal of Operational Research, vol. 134, no. 3, pp. 592–605, 2001.

    Article  MATH  Google Scholar 

  28. M. Kryszkiewicz. Maintenance of Reducts in the Variable Precision Rough Sets Model. ICS Research Report 31/94, Warsaw University of Technology, 1994.

  29. J. Stefanowski. On Rough Set Based Approaches to Induction of Decision Rules. In Rough Sets in Knowledge Discovery, vol. 1, Physica Verlag, Heidelberg, pp. 500–529, 1998.

    Google Scholar 

  30. H. S. Nguyen, A. Skowron. Boolean Reasoning for Feature Extraction Problems. In Proceedings of the 10th International Symposium on Foundations of Intelligent Systems, Springer-Verlag, London, UK, pp. 117–126, 1997.

    Google Scholar 

  31. D. S. Yeung, D. G. Chen, E. C. C. Tsang, J. W. T. Lee, X. Z. Wang. On the Generalization of Fuzzy Rough Sets. IEEE Transactions on Fuzzy Systems, vol. 13, no. 3, pp. 343–361, 2005.

    Article  Google Scholar 

  32. W. Z. Wu, W. X. Zhang. Constructive and Axiomatic Approaches of Fuzzy Approximation Operators. Information Sciences, vol. 159, no.3–4, pp. 233–254, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  33. U. Höhle. Quotients with Respect to Similarity Relations. Fuzzy Sets and Systems, vol. 27, no. 1, pp. 31–44, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  34. P. Srinivasan, M. E. Ruiz, D. H. Kraft, J. Chen. Volcabulary Mining for Information Retrieval: Rough Sets and Fuzzy Sets. Information Processing & Management, vol. 37, no. 1, pp. 15–38, 1998.

    Article  Google Scholar 

  35. Y. Y. Yao. Combination of Rough and Fuzzy Sets Based on α-Level Sets. In Rough Sets and Data Mining: Analysis of Imprecise Data, T. Y. Lin, N. Cereone (eds.), Kluwer Academic Publishers, pp. 301–321, 1997.

  36. A. M. Radzikowska, E. E. Kerre. A Comparative Study of Fuzzy Rough Sets. Fuzzy Sets and Systems, vol. 126, no. 2, pp. 137–155, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  37. M. De Cock, C. Cornelis, E. E. Kerre. Fuzzy Rough Sets: Beyond the Obvious. In IEEE International Conference on Fuzzy Systems. vol. 1, pp. 103–108, 2004.

    Google Scholar 

  38. H. Thiele, Fuzzy Rough Sets Versus Rough Fuzzy Sets — an Interpretation and a Comparative Study Using Concepts of Modal Logics. Technical report CI-30/98, University of Dortmund, 1998.

  39. W. Z. Wu, Y. Leung, J. S. Mi. On Characterizations of (I,T)-Fuzzy Rough Approximation Operators. Fuzzy Sets and Systems, vol. 154, no. 1, pp. 76–102, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  40. D. Boixader, J. Jacas, J. Recasens. Upper and Lower Approximations of Fuzzy Sets. International Journal of General Systems, vol. 29, no. 4, pp. 555–568, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  41. N. N. Morsi, M. M. Yakout. Axiomatics for Fuzzy Rough Sets. Fuzzy Sets and Systems, vol. 100, no. 1–3, pp. 327–342, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  42. W. Z. Wu, J. S. Mi, W. X. Zhang. Generalized Fuzzy Rough Sets. Information Sciences, vol. 151, pp. 263–282, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  43. J. S. Mi, W. X. Zhang. An Axiomatic Characterization of a Fuzzy Generalization of Rough Sets. Information Sciences, vol. 160, no. 1–4, pp. 235–249, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  44. A. M. Radzikowska, E. E. Kerre. Fuzzy Rough Sets Based on Residuated Lattices. Lecture Notes in Computer Science, Springer Berlin, Heidelberg, vol. 3135, pp. 278–296, 2004.

    Google Scholar 

  45. D. Chen, W. X. Zhang, D. Yeung, E. C. C. Tsang. Rough Approximations on a Complete Completely Distributive Lattice with Applications to Generalized Rough Sets. Information Sciences, vol. 176, no. 13, pp. 1829–1848, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  46. K. Qin, Z. Pei. On the Topological Properties of Fuzzy Rough Sets. Fuzzy Sets and Systems, vol. 151, no. 3, pp. 601–613, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  47. W. Z. Wu. A Study on Relationship Between Fuzzy Rough Approximation Operators and Fuzzy Topological Spaces, Lecture Notes in Artificial Intelligence, Springer-Verlag Heidelberg, vol.3613, pp. 167–174, 2005.

    Google Scholar 

  48. S. Nanda, S. Majumdar. Fuzzy Rough Sets. Fuzzy Sets and Systems, vol. 45, pp. 157–160, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  49. T. B. Iwiński. Algebraic Approach to Rough Sets. Bulletin of the Polish Academy of Science and Mathematics vol. 35, pp. 673–683, 1987.

    MATH  Google Scholar 

  50. W. Pedrycz. Shadowed Sets: Bridging Fuzzy and Rough Sets. In Rough Fuzzy Hybridization: A New Trend in Decision-making, S. K. Pal, A. Skowron (eds.), Springer Verlag, Singapore, pp. 179–199, 1999.

    Google Scholar 

  51. F. E. H. Tay, L. Shen. Economic and Financial Prediction Using Rough Sets Model. European Journal of Operational Research, vol. 141, no. 3, pp. 641–659, 2002.

    Article  MATH  Google Scholar 

  52. A. I. Dimitras, S. H. Zanakis, C. Zopounidis. A Survey of Business Failure with an Emphasis on Prediction Methods and Industrial Applications. European Journal of Operational Research, vol. 90, no. 3, pp. 487–513, 1996.

    Article  MATH  Google Scholar 

  53. R. Slowinski, C. Zopounidis, A. I. Dimitras, R. Susmaga. Rough Set Predictor of Business Failure. In Soft Computing in Financial Engineering, R. A. Ribeiro, H. J. Zimmermann, R. R. Yager, J. Kacprzyk (eds.), Physica-Verlag, Wurzburg, pp. 402–424, 1999.

    Google Scholar 

  54. A. I. Dimitras, R. Slowinski, R. Susmaga, C. Zopounidis. Business Failure Prediction Using Rough Sets. European Journal of Operational Research, vol. 114, no. 2, pp. 263–280, 1999.

    Article  MATH  Google Scholar 

  55. J. R. Quinlan. C4.5: Programs for Machine Learning. Morgan Kaufmann Publishers, San Mateo, CA, 1993.

    Google Scholar 

  56. A. Szladow, D. Mills. Tapping Financial Databases. Business Credit, vol. 95, no. 7, p. 8, 1993.

    Google Scholar 

  57. R. Golan, D. Edwards. Temporal Rules Discovery Using Datalogic/R+ with Stock Market Data. In Proceedings of the International Workshop on Rough Sets and Knowledge Discovery, Springer-Verlag, pp. 74–81, 1993.

  58. R. Golan. Stock Market Analysis Utilizing Rogh Set. Theory. Ph.D. dissertation. Department of Computer Science, University of Regina, Canada, 1995.

    Google Scholar 

  59. W. Ziarko, R. Golan, D. Edwards. An Application of Datalogic/R Knowledge Discovery Tool to Identify Strong Predictive Rules in Stock Market Data. In Proceedings of AAAI Workshop on Knowledge Discovery in Database, Washington DC, pp. 89–101, 1993.

  60. J. Bazan, A. Skowron, P. Synak. Dynamic Reducts As a Tool for Extracting Laws From Decision Tables. In Proceedings of the 8th Symposium on Methodologies for Intelligent Systems, Lecture Notes in Artificial Intelligence, Springer-Verlag, vol. 869, pp. 346–355, 1994.

  61. J. K. Baltzersen. An Attempt to Predict Stock Market Data: A Rough Sets Approach. Master dissertation, Knowledge Systems Group, Department of Computer Systems and Telematics, The Norwegian Institute of Technology, University of Trondheim, 1996.

  62. M. Ruggiero. Turning the Key. Futures, vol. 23, no. 14, pp. 38–40, 1994.

    Google Scholar 

  63. R. Slowinski, C. Zopounidis. Rough Set Sorting of Firms According to Bankruptcy Risk. In Applying Multiple Criteria Aid for Decision to Environmental Management, Kluwer Academic Publishers, Dordrecht, Netherlands, pp. 339–357, 1994.

    Google Scholar 

  64. R. Slowinski, C. Zopounidis. Application of the Rough Set Approach to Evaluation of Bankruptcy Risk. International Journal of Intelligent Systems in Accounting, Finance & Management, vol. 4, no. 1, pp. 27–41, 1995.

    Google Scholar 

  65. K. Farion, W. Michalowski, R. Slowinski, S. Wilk, S. Rubin. Rough Set Methodology in Clinical Practice: Controlled Hospital Trial of the MET System. In Proceedings of the 2004 International Conference on Rough Sets and Current Trends in Computing, Lecture Notes in Artificial Intelligence, Springer-Verlag, Heidelberg, vol. 3066, pp. 805–814, 2004.

    Google Scholar 

  66. F. Ginter, T. Pahikkala, S. Pyysalo, J. Boberg, J. Järvinen, T. Salakoski. Extracting Protein-Protein Interaction Sentences by Applying Rough Set Data Analysis. In Proceedings of the 2004 International Conference on Rough Sets and Current Trends in Computing, Lecture Notes in Artificial Intelligence, Springer-Verlag, Heidelberg, vol. 3066, pp. 780–785, 2004.

    Google Scholar 

  67. M. Ningler, G. Stockmanns, G. Schneider, O. Dressler, E. F. Kochs. Rough Set-based Classification of EEG-Signals to Detect Intraoperative Awareness: Comparison of Fuzzy and Crisp Discretization of Real Value Attributes. In Proceedings of the 2004 International Conference on Rough Sets and Current Trends in Computing, Lecture Notes in Artificial Intelligence, Springer-Verlag, Heidelberg, vol. 3066, pp. 825–834, 2004.

    Google Scholar 

  68. T. Hvidsten, A. Lægreid, J. Komorowski. Learning Rule-based Models of Biological Process from Gene Expression Time Profiles Using Gene Ontology. Bioinformatics, vol. 19, no. 9, pp. 1116–1123, 2003.

    Article  Google Scholar 

  69. H. Midelfart, H. J. Komorowski, K. Nørsett, F. Yadetie, A. K. Sandvik, A. Lægreid. Learning Rough Set Classifiers from Gene Expressions and Clinical Data. Fundamenta Informaticae, vol. 53, no. 2, pp. 155–183, 2002.

    MathSciNet  Google Scholar 

  70. L. Shen, F. E. H. Tay, L. Qu, Y. Shen. Fault Diagnosis Using Rough Sets Theory. Computers in Industry, vol. 43, no. 1, pp. 61–72, 2000.

    Article  Google Scholar 

  71. K. Mannar and D. Ceglarek. Continuous Failure Diagnosis for Assembly Systems Using Rough Set Approach. Annals of the CIRP, vol. 53, no. 1, pp. 39–42, 2004.

    Google Scholar 

  72. S. H. Nguyen, T. T. Nguyen, H. S. Nguyen. Rough Set Approach to Sunspot Classification Problem. In Proceedings of the 2005 International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Copmputing, Lecture Notes in Artificial Intelligence, Springer-Verlag, Heidelberg, vol. 3642, pp. 263–272, 2005.

    Chapter  Google Scholar 

  73. J. F. Peters, Z. Suraj, S. Shan, S. Ramanna, W. Pedrycz, N. Pizzi. Classification of Meteorological Volumetric Radar Data Using Rough Set Methods. Pattern Recognition Letters, vol. 24, no. 6, pp. 911–920, 2003.

    Article  Google Scholar 

  74. J. Jelonek, E. Lukasik, A. Naganowski, R. Slowinski. Inducing Jury’s Preferences in Terms of Acoustic Features of Violin Sounds. In Proceedings of the 2004 International Conference on Artificial Intelligence and Soft Computing, Lecture Notes in Artificial Intelligence, Springer-Verlag, Heidelberg, vol. 3070, pp. 492–497, 2004.

    Google Scholar 

  75. L. Lazareck, S. Ramanna. Classification of Swallowing Sound Signals: A Rough Set Approach. In Proceedings of the 2004 International Conference on Rough Sets and Current Trends in Computing, Lecture Notes in Artificial Intelligence, Springer-Verlag, Heidelberg, vol. 3066, pp. 679–684, 2004.

    Google Scholar 

  76. B. Kostek, P. Szczuko, P. Zwan. Processing of Musical Data Employing Rough Sets and Artificial Neural Networks. In Proceedings of the 2004 International Conference on Rough Sets and Current Trends in Computing, Lecture Notes in Artificial Intelligence, Springer-Verlag, Heidelberg, vol. 3066, pp. 539–548, 2004.

    Google Scholar 

  77. M. P. Hippe. Towards the Classification of Musical Works: A Rough Set Approach. In Proceedings of the 2002 International Conference on Rough Sets and Current Trends in Computing, Lecture Notes in Artificial Intelligence, Springer-Verlag, Heidelberg, vol. 2475, pp. 546–553, 2002.

    Google Scholar 

  78. Q. Shen. Semantics-Preserving Dimensionality Reduction in Intelligent Modelling. In Modelling with Words, J. Lawry, J. Shanahan, A. Ralescu (eds.), Springer, pp. 64–79, 2003.

  79. R. Jensen, Q. Shen. Semantics-Preserving Dimensionality Reduction: Rough and Fuzzy-Rough Based Approaches. IEEE Transactions on Knowledge and Data Engineering, vol. 16, no. 12, pp. 1457–1471, 2004.

    Article  Google Scholar 

  80. R. Jensen, Q. Shen. Fuzzy-Rough Sets Assisted Attribute Selection. IEEE Transactions on Fuzzy Systems, vol. 15, no. 1, pp. 73–89, 2007.

    Article  Google Scholar 

  81. Q. Shen, R. Jensen. Selecting Informative Features with Fuzzy-Rough Sets and Its Application for Complex Systems Monitoring. Pattern Recognition, vol. 37, no. 7, pp. 1351–1363, 2004.

    Article  MATH  Google Scholar 

  82. R. B. Bhatt, M. Gopal. On Fuzzy-Rough Sets Approach to Feature Selection. Pattern Recognition Letters, vol. 26, no. 7, pp. 965–975, 2005.

    Article  Google Scholar 

  83. R. B. Bhatt, M. Gopal. On the Compact Computational Domain of Fuzzy-Rough Sets. Pattern Recognition Letters, vol. 26, no. 11, pp. 1632–1640, 2005.

    Article  Google Scholar 

  84. N. M. Parthalain, R. Jensen, Q. Shen. Fuzzy Entropy-assisted Fuzzy-Rough Feature Selection. In Proceedings of the 2006 IEEE International Conference on Fuzzy Systems, pp. 423–430, 2006.

  85. R. Jensen, Q. Shen. Fuzzy-Rough Data Reduction with Ant Colony Optimization. Fuzzy Sets and Systems, vol. 149, no. 1, pp. 5–20, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  86. L. Zhou, W. Li, Y. Wu. Face Recognition Based on Fuzzy Rough Set Reduction. In Proceedings of the 2006 International Conference on Hybrid Information Technology, vol. 1, pp. 642–646, 2006.

    Article  Google Scholar 

  87. G. C. Y. Tsang, D. Chen, E. C. C. Tsang, J. N. T. Lee, D. S. Yeung, On Attributes Reduction with Fuzz Rough Sets. In Proceedings of the 2005 IEEE International Conference on Systems, Man, and Cybernetics, vol. 3, pp. 2775–2780, 2005.

    Article  Google Scholar 

  88. X. Z. Wang, Y. Ha, D. Chen. On the Reduction of Fuzzy Rough Sets. In Proceedings of the 2005 International Conference on Machine Learning and Cybernetics, vol. 5, pp. 3174–3178, 2005.

    Article  Google Scholar 

  89. Jue, Wang, Ju, Wang. Reduction Algorithms Based on Discernibility Matrix: The Ordered Attributes Method. Journal of Computer Science & Technology, vol. 16, no. 6, pp. 489–504, 2001.

    Article  MATH  Google Scholar 

  90. Q. Hu, D. Yu, Z. Xie, J. Liu. Fuzzy Prolabilistic Approximation Spaces and Their Information Measures. IEEE Transactions on Fuzzy Systems, vol. 14, no. 2, pp. 191–201, 2006.

    Article  Google Scholar 

  91. Q. Hu, D. Yu, Z. Xie. Information-preserving Hybrid Data Reduction Based on Fuzzy-Rough Techniques. Pattern Recognition Letters, vol. 27, no. 5, pp. 414–423, 2006.

    Article  Google Scholar 

  92. A. Mieszkowicz-Rolka, L. Rolka. Variable Precision Fuzzy Rough Sets Model in the Analysis of Process Data. Lecture Notes in Computer Science, Springer, Heidelberg, vol. 3641, pp. 354–363, 2005.

    Google Scholar 

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  1. Department of Computer Science, The University of Wales, Aberystwyth, Ceredigion, SY23 3DB, UK

    Qiang Shen & Richard Jensen

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  1. Qiang Shen
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Correspondence to Qiang Shen.

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This work was partly supported by the UK EPSRC Grant (No. GR/S98603/01).

Qiang Shen received the B.Sc. and M.Sc. degrees in communications and electronic engineering from the National University of Defence Technology, China, and the Ph.D. degree in knowledge-based systems from Heriot-Watt University, Edinburgh, U.K.

He is a professor with the Department of Computer Science at the University of Wales, Aberystwyth, and an honorary fellow at the University of Edinburgh. His research interests include fuzzy and imprecise modeling, model-based inference, pattern recognition, and knowledge refinement and reuse. Professor Shen is an associate editor of the IEEE Transactions on Fuzzy Systems and of the IEEE Transactions on Systems, Man, and Cybernetics (Part B), and an editorial board member of the Fuzzy Sets and Systems Journal amongst others. He has published over 180 papers in academic journals and conferences on topics within artificial intelligence and related areas.

Richard Jensen received the B.Sc. degree in computer science from Lancaster University, U.K., and the M.Sc. and Ph.D. degrees in artificial intelligence from the University of Edinburgh, U.K.

He is a research fellow with the Department of Computer Science at the University of Wales, Aberystwyth, working in the Advanced Reasoning Group. His research interests include rough and fuzzy set theory, pattern recognition, information retrieval, feature selection, and swarm intelligence. He has published over 20 papers in these areas.

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Shen, Q., Jensen, R. Rough sets, their extensions and applications. Int J Automat Comput 4, 217–228 (2007). https://doi.org/10.1007/s11633-007-0217-y

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