A Rough Fuzzy Perspective to Dimensionality Reduction

  • Alessio FeroneEmail author
  • Alfredo Petrosino
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7627)


Rough set theory and fuzzy logic are mathematical frameworks for granular computing forming a theoretical basis for the treatment of uncertainty in many real–world problems. The focus of rough set theory is on the ambiguity caused by limited discernibility of objects in the domain of discourse; granules are formed as objects and are drawn together by the limited discernibility among them. On the other hand, membership functions of fuzzy sets enables efficient handling of overlapping classes. The hybrid notion of rough fuzzy sets comes from the combination of these two models of uncertainty and helps to exploit, at the same time, properties like coarseness and vagueness. We describe a model of the hybridization of rough and fuzzy sets, that allows for further refinements of rough fuzzy sets and show its application to the task of unsupervised feature selection.


Rough fuzzy sets Modelling hierarchies Unsupervised feature selection 


  1. 1.
    Bakar, A.A., Sulaiman, M.N., Othman, M., Selamat, M.H.: Finding minimal reduct with binary integer programming in data mining. In: Proceedings of the TENCON, pp. 141–149 (2000)Google Scholar
  2. 2.
    Bellman, R.: Adaptive Control Processes: A Guided Tour. Princeton University Press, Princeton (1961)CrossRefzbMATHGoogle Scholar
  3. 3.
    Chanas, S., Kuchta, D.: Further remarks on the relation between rough and fuzzy sets. Fuzzy Sets Syst. 47(3), 391–394 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Chen, D., Tsang, E.C.C., Yeung, D.S., Wang, X.: The parameterization reduction of soft sets and its applications. Int. J. Comput. Math. 49, 757–763 (2005)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Das, S.K.: Feature selection with a linear dependence measure. IEEE Trans. Comput. 20, 1106–1109 (1971)CrossRefGoogle Scholar
  6. 6.
    Dash, M., Liu, H.: Unsupervised feature selection. In: Proceedings of the Pacific and Asia Conference on Knowledge Discovery and Data Mining, pp. 110–121 (2000)Google Scholar
  7. 7.
    Dash, M., Liu, H.: Feature selection for classification. Intell. Data Anal. 1(3), 131–156 (1997)CrossRefGoogle Scholar
  8. 8.
    Devijver, P., Kittler, J.: Pattern Recognition: A Statistical Approach. Prentice Hall, London (1982)zbMATHGoogle Scholar
  9. 9.
    Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. Int. J. Gen Syst 17(2–3), 191–209 (1990)CrossRefzbMATHGoogle Scholar
  10. 10.
    Grzymala-Busse, J.W.: MLEM2-discretization during rule induction. In: Procedings of IIPWM (2003)Google Scholar
  11. 11.
    Hall, M.A.: Correlation-based feature selection for discrete and numeric class machine learning. In: Proceedings of the 17th International Conference on Machine Learning, pp. 359–366 (2000)Google Scholar
  12. 12.
    Hong, T.-P., Tseng, L.-H., Wang, S.-L.: Learning rules from incomplete training examples by rough sets. Expert Syst. Appl. 22, 285–293 (2002)CrossRefGoogle Scholar
  13. 13.
    Hu, X.: Using rough sets theory and database operations to construct a good ensemble of classifiers for data mining applications. In: Proceedings of ICDM, pp. 233–240 (2001)Google Scholar
  14. 14.
    Hu, X., Lin, T.Y., Jianchao, J.: A new rough sets model based on database systems. Fundamenta Informaticae 20, 1–18 (2004)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Jensen, R., Shen, Q.: Interval-valued fuzzy-rough feature selection in datasets with missing values. In: IEEE International Conference on Fuzzy Systems, pp. 610–615 (2009)Google Scholar
  16. 16.
    Jensen, R., Shen, Q.: New approaches to fuzzy-rough feature selection. IEEE Trans. Fuzzy Syst. 17(4), 824–838 (2009)CrossRefGoogle Scholar
  17. 17.
    Jensen, R., Shen, Q.: Semantics-preserving dimensionality reduction: rough and fuzzy-rough-based approaches. IEEE Trans. Knowl. Data Eng. 16(12), 1457–1471 (2004)CrossRefGoogle Scholar
  18. 18.
    Khoo, L.P., Tor, S.B., Zhai, L.Y.: A rough set-based approach for classification and rule induction. Int. J. Adv. Manuf. Technol. 15, 438–444 (1999)CrossRefGoogle Scholar
  19. 19.
    Lin, T.Y., Cercone, N.: Rough sets and Data Mining: Analysis of Imprecise Data. Kluwer Academic Publishers, Boston (1997)zbMATHGoogle Scholar
  20. 20.
    Maji, P., Pal, S.K.: Feature selection using f-information measures in fuzzy approximation spaces. IEEE Trans. Knowl. Data Eng. 22(6), 854–867 (2010)CrossRefGoogle Scholar
  21. 21.
    Mitchell, T.: Machine Learning. McGraw-Hill, Maidenhead (1997)zbMATHGoogle Scholar
  22. 22.
    Mitra, P., Murthy, C.A., Pal, S.K.: Unsupervised feature selection using feature similarity. IEEE Trans. Pattern Anal. Mach. Intell. 24(4), 1–13 (2002)Google Scholar
  23. 23.
    Pal, S.K., De, R.K., Basak, J.: Unsupervised feature evaluation: a neuro-fuzzy approach. IEEE Trans. Neural Network. 11, 366–376 (2000)CrossRefGoogle Scholar
  24. 24.
    Parthaláin, N.M., Shen, Q., Jensen, R.: A distance measure approach to exploring the rough set boundary region for attribute reduction. IEEE Trans. Knowl. Data Eng. 22(3), 305–317 (2010)CrossRefGoogle Scholar
  25. 25.
    Parthaláin, N.M., Jensen, R.: Measures for unsupervised fuzzy-rough feature selection. Int. J. Hybrid Intell. Syst. 7(4), 249–259 (2010)CrossRefzbMATHGoogle Scholar
  26. 26.
    Pawlak, Z.: Rough sets. Int. J. Comput. Inform. Sci. 11, 341–356 (1982)CrossRefzbMATHGoogle Scholar
  27. 27.
    Pawlak, Z.: Granularity of knowledge, indiscernibility and rough sets. In: Proceedings of IEEE International Conference on Fuzzy Systems, pp. 106–110 (1998)Google Scholar
  28. 28.
    Pedrycz, W., Gomide, F.: Fuzzy Systems Engineering: Toward Human-Centric Computing. Wiley, Hoboken (2007)CrossRefGoogle Scholar
  29. 29.
    Petrosino, A., Ferone, A.: Feature discovery through hierarchies of rough fuzzy sets. In: Chen, S.-M., Pedrycz, W. (eds.) Granular Computing and Intelligent Systems: Design with Information Granules of Higher Order and Higher Type. Springer, Heidelberg (2011)Google Scholar
  30. 30.
    Questier, F., Rollier, I.A., Walczak, B., Massart, D.L.: Application of rough set theory to feature selection for unsupervised clustering. Chemometr. Intell. Lab. Syst. 63, 55–167 (2002)CrossRefGoogle Scholar
  31. 31.
    Shen, Q., Chouchoulas, A.: A modular approach to generating fuzzy rules with reduced attributes for the monitoring of complex systems. Eng. Appl. Artif. Intell. 13(3), 263–278 (2002)CrossRefGoogle Scholar
  32. 32.
    Swiniarski, R.W., Skowron, A.: Rough set methods in feature selection and recognition. Pattern Recogn. Lett. 24, 833–849 (2003)CrossRefzbMATHGoogle Scholar
  33. 33.
    Thangavel, K., Shen, Q., Pethalakshmi, A.: Application of clustering for feature selection based on rough set theory approach. AIML J. 6(1), 19–27 (2005)Google Scholar
  34. 34.
    Thangavel, K., Pethalakshmi, A., Jaganathan, P.: em A comparative analysis of feature selection algorithms based on rough set theory. Int. J. Soft Comput. 1(4), 288–294 (2006)Google Scholar
  35. 35.
    Thangavel, K., Pethalakshmi, A.: Performance analysis of accelerated Quickreduct algorithm. In: Proceedings of International Conference on Computational Intelligence and Multimedia Applications, pp. 318–322 (2007)Google Scholar
  36. 36.
    Thangavel, K., Pethalakshmi, A.: Feature selection for medical database using rough system. Int. J. Artif. Intell. Mach. Learn. 6, 11–17 (2005)Google Scholar
  37. 37.
    Tsai, Y.-C., Cheng, C.-H., Chang, J.-R.: Entropy-based fuzzy rough classification approach for extracting classification rules. Expert Syst. Appl. 31(2), 436–443 (2006)CrossRefGoogle Scholar
  38. 38.
    Tsang, E.C.C., Chen, D., Yeung, D.S., Wang, X.-Z., Lee, J.: Attributes reduction using fuzzy rough sets. IEEE Trans. Fuzzy Syst. 16(5), 1130–1141 (2008)CrossRefGoogle Scholar
  39. 39.
    Velayutham, C., Thangavel, K.: Unsupervised quick reduct algorithm using rough set theory. J. Electron. Sci. Technol. 9(3), 193–201 (2011)Google Scholar
  40. 40.
    Witten, I.H., Frank, E.: Data Mining: Practical Machine Learning Tools with Java Implementations. Morgan Kaufmann, San Francisco (2000)Google Scholar
  41. 41.
    Zadeh, L.: Fuzzy sets. Inf. Control 8, 338–353 (1964)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Science and TechnologyUniversity of Naples ParthenopeNaplesItaly

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