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Dual Rough Approximations in Information Tables with Missing Values

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Rough Sets, Fuzzy Sets, Data Mining and Granular Computing (RSFDGrC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6743))

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Abstract

A method of possible equivalence classes has been developed under information tables with missing values. To deal with imprecision of rough approximations that comes from missing values, the concepts of certainty and possibility are used. When an information table contains missing values, two rough approximations, certain and possible ones, are obtained. The actual rough approximation lies between the certain and possible rough approximations. The method gives the same results as a method of possible worlds. This justifies the method of possible equivalence classes. Furthermore, the method is free from the restriction that missing values may occur to only some specified attributes. Hence, we can use the method of possible equivalence classes to obtain rough approximations between arbitrary sets of attributes having missing values.

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References

  1. Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley Publishing Company, Reading (1995)

    MATH  Google Scholar 

  2. Bosc, P., Duval, L., Pivert, O.: An Initial Approach to the Evaluation of Possibilistic Queries Addressed to Possibilistic Databases. Fuzzy Sets and Systems 140, 151–166 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  3. Grahne, G.: The Problem of Incomplete Information in Relational Databases. LNCS, vol. 554. Springer, Heidelberg (1991)

    MATH  Google Scholar 

  4. Greco, S., Matarazzo, B., Słowiński, R.: Handling missing values in rough set analysis of multi-attribute and multi-criteria decision problems. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 146–157. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  5. Grzymala-Busse, J.W.: Data with Missing Attribute Values: Generalization of Indiscernibility Relation and Rule Induction. Transactions on Rough Sets I, 78–95 (2004)

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. Imielinski, T., Lipski, W.: Incomplete Information in Relational Databases. Journal of the ACM 31, 761–791 (1984)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  9. Lipski, W.: On Semantics Issues Connected with Incomplete Information Databases. ACM Transactions on Database Systems 4, 262–296 (1979)

    Article  Google Scholar 

  10. Lipski, W.: On Databases with Incomplete Information. Journal of the ACM 28, 41–70 (1981)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  12. 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 (LNAI), vol. 3558, pp. 227–239. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  13. Nakata, M., 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 (LNAI), vol. 3641, pp. 325–334. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  14. Nakata, M., Sakai, H.: Lower and Upper Approximations in Data Tables Containing Possibilistic Information. Transactions on Rough Sets VII, 170–189 (2007)

    MathSciNet  MATH  Google Scholar 

  15. Nakata, M., Sakai, H.: Applying Rough Sets to Information Tables Containing Probabilistic Values. In: Torra, V., Narukawa, Y., Yoshida, Y. (eds.) MDAI 2007. LNCS (LNAI), vol. 4617, pp. 282–294. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  16. Nakata, M., Sakai, H.: Rough Sets Approximations in Data Tables Containing Missing Values. In: Proceedings of FUZZ-IEEE 2008, pp. 673–680. IEEE Press, New York (2008)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  18. Paredaens, J., De Bra, P., Gyssens, M., Van Gucht, D.: The Structure of the Relational Database Model. Springer, Heidelberg (1989)

    Book  MATH  Google Scholar 

  19. Parsons, S.: Current Approaches to Handling Imperfect Information in Data and Knowledge Bases. IEEE Transactions on Knowledge and Data Engineering 8, 353–372 (1996)

    Article  Google Scholar 

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

    Book  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  22. 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 

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

    MATH  Google Scholar 

  24. Slowiński, R., Stefanowski, J.: Rough Classification in Incomplete Information Systems. Mathematical and Computer Modelling 12, 1347–1357 (1989)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  26. Szczuka, M., Kryszkiewicz, M., Ramanna, S., Jensen, R., Hu, Q. (eds.): RSCTC 2010. LNCS, vol. 6086. Springer, Heidelberg (2010)

    Google Scholar 

  27. Yu, J., Greco, S., Lingras, P., Wang, G., Skowron, A. (eds.): RSKT 2010. LNCS, vol. 6401. Springer, Heidelberg (2010)

    Google Scholar 

  28. Zimányi, E., Pirotte, A.: Imperfect Information in Relational Databases. In: Motro, A., Smets, P. (eds.) Uncertainty Management in Information Systems: From Needs to Solutions, pp. 35–87. Kluwer Academic Publishers, Boston (1997)

    Chapter  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. State University Higher School of Economics, Pokrovskiy Bd. 11, 109028, Moscow, Russia

    Sergei O. Kuznetsov

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

    Dominik Ślęzak

  3. Department of Computer Science, University of Regina, 3737 Wascana Parkway, S4S 0A2, Regina, SK, Canada

    Daryl H. Hepting

  4. Birbeck University of London, Malet Street, WC1E 7HX, London, UK

    Boris G. Mirkin

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Nakata, M., Sakai, H. (2011). Dual Rough Approximations in Information Tables with Missing Values. In: Kuznetsov, S.O., Ślęzak, D., Hepting, D.H., Mirkin, B.G. (eds) Rough Sets, Fuzzy Sets, Data Mining and Granular Computing. RSFDGrC 2011. Lecture Notes in Computer Science(), vol 6743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21881-1_8

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  • DOI: https://doi.org/10.1007/978-3-642-21881-1_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21880-4

  • Online ISBN: 978-3-642-21881-1

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