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Lower and Upper Approximations in Data Tables Containing Possibilistic Information

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Transactions on Rough Sets VII

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 4400))

Abstract

An extended method of rough sets, called a method of weighted equivalence classes, is applied to a data table containing imprecise values expressed in a possibility distribution. An indiscerniblity degree between objects is calculated. A family of weighted equivalence classes is obtained via indiscernible classes from a binary relation for indiscernibility between objects. Each equivalence class in the family is accompanied by a possibilistic degree to which it is an actual one. By using the family of weighted equivalence classes we derive a lower approximation and an upper approximation. These approximations coincide with those obtained from methods of possible worlds. Therefore, the method of weighted equivalence classes is justified.

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References

  1. Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, 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  MATH  MathSciNet  Google Scholar 

  3. Bosc, P., Liétard, N., Pivert, O.: About the Processing of Possibilistic Queries Involving a Difference Operation. Fuzzy Sets and systems 157, 1622–1640 (2006)

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  5. 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)

    Google Scholar 

  6. Greco, S., Matarazzo, B., Slowinski, R.: Rough Sets Theory for Multicriteria Decision Analysis. European Journal of Operational Research 129, 1–47 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Grzymala-Busse, J.W.: On the Unknown Attribute Values in Learning from Examples. In: Raś, Z.W., Zemankova, M. (eds.) ISMIS 1991. LNCS, vol. 542, pp. 368–377. Springer, Heidelberg (1991)

    Google Scholar 

  8. Grzymala-Busse, J.W.: Data with Missing Attribute Values: Generalization of Indiscernibility Relation and Rule Induction. Transactions on Rough Sets 1, 78–95 (2004)

    Google Scholar 

  9. Grzymala-Busse, J.W.: Characteristic Relations for Incomplete Data: A Generalization of the Indiscernibility Relation. Transactions on Rough Sets 4, 58–68 (2005)

    Article  Google Scholar 

  10. Grzymala-Busse, J.W., Hu, M.: A Comparison of Several Approaches to Missing Attribute Values in Data Mining. In: Ziarko, W., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 378–385. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  11. Grzymala-Busse, J.W., Rzasa, W.: Local and Global Approximations for Incomplete Data. In: Greco, S., et al. (eds.) RSCTC 2006. LNCS (LNAI), vol. 4259, pp. 244–253. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  12. Imielinski, T.: Incomplete Information in Logical Databases. Data Engineering 12, 93–104 (1989)

    Google Scholar 

  13. Imielinski, T., Lipski, W.: Incomplete Information in Relational Databases. Journal of the ACM 31(4), 761–791 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  14. Kryszkiewicz, M.: Rough Set Approach to Incomplete Information Systems. Information Sciences 112, 39–49 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  15. Kryszkiewicz, M.: Properties of Incomplete Information Systems in the framework of Rough Sets. In: Polkowski, L., Skowron, A. (eds.) Rough Set in Knowledge Discovery 1: Methodology and Applications. Studies in Fuzziness and Soft Computing, vol. 18, pp. 422–450. Physica, Heidelberg (1998)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  17. Kryszkiewicz, M., Rybiński, H.: Data Mining in Incomplete Information Systems from Rough Set Perspective. In: Polkowski, L., Tsumoto, S., Lin, T.Y. (eds.) Rough Set Methods and Applications. Studies in Fuzziness and Soft Computing, vol. 56, pp. 568–580. Physica, Heidelberg (2000)

    Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  19. Latkowski, R.: Flexible Indiscernibility Relations for Missing Values. Fundamenta Informaticae 67, 131–147 (2005)

    MATH  MathSciNet  Google Scholar 

  20. Nakata, N., Sakai, H.: Rough-set-based approaches to data containing incomplete information: possibility-based cases. In: Nakamatsu, K., Abe, J.M. (eds.) Advances in Logic Based Intelligent Systems. Frontiers in Artificial Intelligence and Applications, vol. 132, pp. 234–241. IOS Press, Amsterdam (2005)

    Google Scholar 

  21. Nakata, N., 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)

    Google Scholar 

  22. Nakata, N., Sakai, H.: Rough Sets Handling Missing Values Probabilistically Interpreted. In: Ślęzak, D., et al. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 325–334. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  23. Nakata, N., Sakai, H.: Applying Rough Sets to Data Tables Containing Probabilistic Information. In: Proceedings of 4th Workshop on Rough Sets and Kansei Engineering, Tokyo, Japan, pp. 50–53 (2005)

    Google Scholar 

  24. Nakata, N., Sakai, H.: Applying Rough Sets to Data Tables Containing Imprecise Information Under Probabilistic Interpretation. In: Greco, S., et al. (eds.) RSCTC 2006. LNCS (LNAI), vol. 4259, pp. 213–223. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

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

    Google Scholar 

  26. 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 

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

    MATH  Google Scholar 

  28. Pawlak, Z.: Some Issues on Rough Sets. Transactions on Rough Sets 1, 1–58 (2004)

    MathSciNet  Google Scholar 

  29. Pawlak, Z., Skowron, A.: Rudiments of Rough Sets. Information Sciences 177, 3–27 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  30. Pawlak, Z., Skowron, A.: Rough Sets: Some Extensions. Information Sciences 177, 28–40 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  31. Pawlak, Z., Skowron, A.: Rough Sets and Boolean Reasoning. Information Sciences 177, 41–73 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  32. Ras, Z.W., Joshi, S.: Query Approximate Answering System for an Incomplete DKBS. Fundamenta Informaticae 30, 313–324 (1997)

    MATH  MathSciNet  Google Scholar 

  33. Sakai, H.: Some Issues on Nondeterministic Knowledge Bases with Incomplete Information. In: Polkowski, L., Skowron, A. (eds.) RSCTC 1998. LNCS (LNAI), vol. 1424, pp. 424–431. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

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

    MathSciNet  Google Scholar 

  35. 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)

    Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  38. Stefanowski, J., Tsoukiàs, A.: On the Extension of Rough Sets under Incomplete Information. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 73–81. Springer, Heidelberg (1999)

    Google Scholar 

  39. Stefanowski, J., Tsoukiàs, A.: Valued Tolerance and Decision Rules. In: Ziarko, W., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 212–219. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  41. 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, Dordrecht (1997)

    Google Scholar 

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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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James F. Peters Andrzej Skowron Victor W. Marek Ewa Orłowska Roman Słowiński Wojciech Ziarko

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Nakata, M., Sakai, H. (2007). 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. (eds) Transactions on Rough Sets VII. Lecture Notes in Computer Science, vol 4400. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71663-1_11

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  • DOI: https://doi.org/10.1007/978-3-540-71663-1_11

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