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Rough Sets under Non-deterministic Information

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Rough Sets and Knowledge Technology (RSKT 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5589))

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Abstract

A method of possible equivalence classes, described in [14], is extended under non-deterministic information. The method considers both indiscernibility and discernibility of non-deterministic values by using possible equivalence classes. As a result, the method gives the same results as the method of possible worlds. Furthermore, maximal possible equivalences are introduced in order to effectively calculate rough approximations. We can use the method of possible equivalence classes to obtain rough approximations between arbitrary sets of attributes containing non-deterministic values.

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References

  1. Greco, S., Matarazzo, B., Slowinski, R.: Handling Missing Values in Rough Set Analysis of Multi-attribute and Multi-criteria Decision Problem. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 146–157. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  2. Grzymala-Busse, J.W.: MLEM2: A New Algorithm for Rule Induction from Imperfect Data. In: Proceedings of the IPMU 2002, 9th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Annecy, France, pp. 243–250 (2002)

    Google Scholar 

  3. Grzymała-Busse, J.W.: Data with missing attribute values: Generalization of indiscernibility relation and rule induction. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B.z., Świniarski, R.W., Szczuka, M.S. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 78–95. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  4. Grzymala-Busse, J.W.: Characteristic relations for incomplete data: A generalization of the indiscernibility relation. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets IV. LNCS (LNAI), vol. 3700, pp. 58–68. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  5. Guan, Y.-Y., Wang, H.-K.: Set-valued Information Systems. Information Sciences 176, 2507–2525 (2006)

    Article  MATH  Google Scholar 

  6. Kryszkiewicz, M.: Rules in Incomplete Information Systems. Information Sciences 113, 271–292 (1999)

    Article  MATH  Google Scholar 

  7. Latkowski, R.: On Decomposition for Incomplete Data. Fundamenta Informaticae 54, 1–16 (2003)

    MATH  Google Scholar 

  8. Leung, Y., Li, D.: Maximum Consistent Techniques for Rule Acquisition in Incomplete Information Systems. Information Sciences 153, 85–106 (2003)

    Article  MATH  Google Scholar 

  9. Nakata, M., Sakai, H.: Checking whether or not rough-set-based methods to incomplete data satisfy a correctness criterion. In: Torra, V., Narukawa, Y., Miyamoto, S. (eds.) MDAI 2005. LNCS, vol. 3558, pp. 227–239. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  10. Nakata, N., Sakai, H.: Rough Sets Handling Missing Values Probabilistically Interpreted. In: Ślęzak, D., Wang, G., Szczuka, M.S., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS, vol. 3641, pp. 325–334. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  11. Nakata, N., Sakai, H.: Applying Rough Sets to Data Tables Containing Imprecise Information Under Probabilistic Interpretation. In: Greco, S., Hata, Y., Hirano, S., Inuiguchi, M., Miyamoto, S., Nguyen, H.S., Słowiński, R. (eds.) RSCTC 2006. LNCS, vol. 4259, pp. 213–223. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  12. Nakata, N., Sakai, H.: Lower and upper approximations in data tables containing possibilistic information. In: Peters, J.F., Skowron, A., Marek, V.W., Orłowska, E., Słowiński, R., Ziarko, W.P. (eds.) Transactions on Rough Sets VII. LNCS, vol. 4400, pp. 170–189. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  13. Nakata, N., Sakai, H.: Applying rough sets to information tables containing probabilistic values. In: Torra, V., Narukawa, Y., Yoshida, Y. (eds.) MDAI 2007. LNCS, vol. 4617, pp. 282–294. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  14. Nakata, N., Sakai, H.: Rough Sets Approximations in Data Tables Containing Missing Values. In: Proceedings of FUZZ-IEEE 2008. IEEE Press, Los Alamitos (2008)

    Google Scholar 

  15. Orłowska, E., Pawlak, Z.: Representation of Nondeterministic Information. Theoretical Computer Science 29, 313–324 (1984)

    MATH  Google Scholar 

  16. Parsons, S.: Current Approaches to Handling Imperfect Information in Data and Knowledge Bases. IEEE Transactions on Knowledge and Data Engineering 83, 353–372 (1996)

    Article  Google Scholar 

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

    Book  MATH  Google Scholar 

  18. Sakai, H.: Effective Procedures for Handling Possible Equivalence Relation in Non-deterministic Information Systems. Fundamenta Informaticae 48, 343–362 (2001)

    MATH  Google Scholar 

  19. Sakai, H., Nakata, M.: An Application of Discernibility Functions to Generating Minimal Rules in Non-deterministic Information Systems. Journal of Advanced Computational Intelligence and Intelligent Informatics 10, 695–702 (2006)

    Article  Google Scholar 

  20. Sakai, H., Okuma, A.: Basic Algorithms and Tools for Rough Non-deterministic Information Systems. Transactions on Rough Sets 1, 209–231 (2004)

    MATH  Google Scholar 

  21. Słowiński, R., Stefanowski, J.: Rough Classification in Incomplete Information Systems. Mathematical and Computer Modelling 12(10/11), 1347–1357 (1989)

    Google Scholar 

  22. Stefanowski, J., Tsoukiàs, A.: Incomplete Information Tables and Rough Classification. Computational Intelligence 17(3), 545–566 (2001)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Management and Information Science, Josai International University, 1 Gumyo, Togane, Chiba, 283-8555, Japan

    Michinori Nakata

  2. Department of Mathematics and Computer Aided Sciences, Faculty of Engineering, Kyushu Institute of Technology, Tobata, Kitakyushu, 804-8550, Japan

    Hiroshi Sakai

Authors
  1. Michinori Nakata
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  2. Hiroshi Sakai
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Editor information

Editors and Affiliations

  1. Faculty of Engineering and Surveying and Engineering, University of Southern Queensland, QLD 4350, Australia

    Peng Wen

  2. School of Information Technology, Queensland University of Technology, QLD 4001, Brisbane, Australia

    Yuefeng Li

  3. Institute of Mathematics, Warsaw University of Technology, Koszykowa 86, 02008, Warsaw, Poland

    Lech Polkowski

  4. Department of Computer Science, University of Regina, S4S 0A2, Regina, Saskatchewan, Canada

    Yiyu Yao

  5. Faculty of Medicine, Department of Medical Informatics, Shimane University, 89-1 Enya-cho, Izumo, 693-8501, Shimane, Japan

    Shusaku Tsumoto

  6. Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, China

    Guoyin Wang

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© 2009 Springer-Verlag Berlin Heidelberg

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Nakata, M., Sakai, H. (2009). Rough Sets under Non-deterministic Information. In: Wen, P., Li, Y., Polkowski, L., Yao, Y., Tsumoto, S., Wang, G. (eds) Rough Sets and Knowledge Technology. RSKT 2009. Lecture Notes in Computer Science(), vol 5589. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02962-2_10

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  • DOI: https://doi.org/10.1007/978-3-642-02962-2_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02961-5

  • Online ISBN: 978-3-642-02962-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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