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On Classifying Mappings Induced by Granular Structures

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Transactions on Rough Sets IX

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 5390))

Abstract

In this work the subject of granular computing is pursued beyond the content of the previous paper [21]. We study here voting on a decision by granules of training objects, granules of decision rules, granules of granular reflections of training data, and granules of decision rules induced from granular reflections of training data. This approach can be perceived as a direct mapping of the training data on test ones which is induced by granulation of knowledge on the training data. Some encouraging results were already presented in [21], and here the subject is pursued systematically.

Granules of knowledge are defined and computed according to a previously used scheme due to Polkowski in the framework of theory of rough inclusions.

On the basis of presented results, one is justified in concluding that the presented methods offer a very good quality of classification, comparable fully with best results obtained by other rough set based methods, like templates, adaptive methods, hybrid methods etc.

This work is an extension of the work [20] presented by the authors at RSEISP07 International Conference.

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References

  1. Artiemjew, P.: On classification of data by means of rough mereological granules of objects and rules. In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds.) RSKT 2008. LNCS, vol. 5009, pp. 221–228. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  2. Artiemjew, P.: Classifiers from granulated data sets: Concept dependent and layered granulation. In: Proceedings RSKD 2007. Workshop at ECML/PKDD 2007, pp. 1–9. Warsaw Univ. Press, Warsaw (2007)

    Google Scholar 

  3. Bazan, J.G.: A comparison of dynamic and non–dynamic rough set methods for extracting laws from decision tables. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery, vol. 1, pp. 321–365. Physica Verlag, Heidelberg (1998)

    Google Scholar 

  4. Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht (1998)

    Book  MATH  Google Scholar 

  5. Hoa, N.S.: Regularity analysis and its applications in Data Mining. In: Polkowski, L., Tsumoto, S., Lin, T.Y. (eds.) Rough Set Methods and Applications, pp. 289–378. Physica Verlag, Heidelberg (2000)

    Google Scholar 

  6. Pawlak, Z.: Rough sets. Int. J. Computer and Information Sci. 11, 341–356 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  7. Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer, Dordrecht (1991)

    Book  MATH  Google Scholar 

  8. Polkowski, L.: Rough Sets. Mathematical Foundations. Physica Verlag, Heidelberg (2002)

    Book  MATH  Google Scholar 

  9. Poincare, H.: Science and Hypothesis. Walter Scott Publ., London (1905)

    MATH  Google Scholar 

  10. Polkowski, L.: Rough Sets. Mathematical Foundations. Physica Verlag, Heidelberg (2002)

    Book  MATH  Google Scholar 

  11. Polkowski, L.: A rough set paradigm for unifying rough set theory and fuzzy set theory (a plenary lecture). In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.) RSFDGrC 2003. LNCS, vol. 2639, pp. 70–78. Springer, Heidelberg (2003); also Fundamenta Informaticae 54, 67–88 (2003)

    Chapter  Google Scholar 

  12. Polkowski, L.: Toward rough set foundations. Mereological approach (a plenary lecture). In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS, vol. 3066, pp. 8–25. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  13. Polkowski, L.: Formal granular calculi based on rough inclusions (a feature talk). In: [24], pp. 57–62

    Google Scholar 

  14. Polkowski, L.: A model of granular computing with applications (a feature talk). In: [25], pp. 9–16

    Google Scholar 

  15. Polkowski, L.: The paradigm of granular rough computing. In: Proceedings ICCI 2007. 6th IEEE Intern. Conf. on Cognitive Informatics, Lake Tahoe NV, USA, August 2007, pp. 145–163. IEEE Computer Society, Los Alamitos (2007)

    Google Scholar 

  16. Polkowski, L.: Granulation of knowledge in decision systems: The approach based on rough inclusions. The method and its applications. In: Kryszkiewicz, M., Peters, J.F., Rybinski, H., Skowron, A. (eds.) RSEISP 2007. LNCS, vol. 4585, pp. 271–279. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  17. Polkowski, L.: A Unified approach to granulation of knowledge and granular computing based on rough mereology: A Survey. In: Pedrycz, W., Skowron, A., Kreinovich, V. (eds.) Handbook of Granular Computing, ch. 16. John Wiley, NY (2008)

    Google Scholar 

  18. Polkowski, L.: On the idea of using granular rough mereological structures in classification of data. In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds.) RSKT 2008. LNCS, vol. 5009, pp. 213–220. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  19. Polkowski, L.: Rough mereology as a tool in analysis of vagueness. In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds.) RSKT 2008. LNCS, vol. 5009, pp. 205–212. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  20. Polkowski, L., Artiemjew, P.: On granular rough computing: Factoring clasifiers through granular structures. In: Kryszkiewicz, M., Peters, J.F., Rybinski, H., Skowron, A. (eds.) RSEISP 2007. LNCS, vol. 4585, pp. 280–289. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  21. Polkowski, L., Artiemjew, P.: A study in granular computing: On classifiers induced from granular reflections of data. In: Peters, J.F., et al. (eds.) Transactions on Rough Sets. LNCS, vol. 5390. Springer, Heidelberg (2008)

    Google Scholar 

  22. Polkowski, L., Skowron, A.: Rough mereology. In: Ras, Z., Zemankova, M. (eds.) ISMIS 1994. LNCS (LNAI), vol. 869, pp. 85–94. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  23. Polkowski, L., Skowron, A.: Rough mereology: a new paradigm for approximate reasoning. International Journal of Approximate Reasoning 15(4), 333–365 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  24. Proceedings of IEEE 2005 Conference on Granular Computing, GrC 2005, Beijing, China, July 2005. IEEE Press, Los Alamitos (2005)

    Google Scholar 

  25. Proceedings of IEEE 2006 Conference on Granular Computing, GrC 2006, Atlanta, USA, May 2006. IEEE Press, Los Alamitos (2006)

    Google Scholar 

  26. Skowron, A. et al.: RSES, http://logic.mimuw.edu.pl/~rses/

  27. UCI Repository, http://www.ics.uci.edu/~mlearn/databases/

  28. Wróblewski, J.: Adaptive aspects of combining approximation spaces. In: Pal, S.K., Polkowski, L., Skowron, A. (eds.) Rough – Neural Computing. Techniques for Computing with Words, pp. 139–156. Springer, Berlin (2004)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Polish–Japanese Institute of Information Technology, Koszykowa 86, 02008, Warszawa, Poland

    Lech Polkowski

  2. University of Warmia and Mazury, Zolnierska 14, 10560, Olsztyn, Poland

    Piotr Artiemjew

Authors
  1. Lech Polkowski
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  2. Piotr Artiemjew
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Manitoba, R3T 5V6, Winnipeg, Manitoba, Canada

    James F. Peters

  2. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

  3. Institute of Computer Science, Warsaw University of Technology, Nowowoiejska 15/19, 00-665, Warsaw, Poland

    Henryk Rybiński

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Polkowski, L., Artiemjew, P. (2008). On Classifying Mappings Induced by Granular Structures. In: Peters, J.F., Skowron, A., Rybiński, H. (eds) Transactions on Rough Sets IX. Lecture Notes in Computer Science, vol 5390. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89876-4_15

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  • DOI: https://doi.org/10.1007/978-3-540-89876-4_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89875-7

  • Online ISBN: 978-3-540-89876-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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