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Pawlak’s Many Valued Information System, Non-deterministic Information System, and a Proposal of New Topics on Information Incompleteness Toward the Actual Application

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Thriving Rough Sets

Part of the book series: Studies in Computational Intelligence ((SCI,volume 708))

Abstract

This chapter considers Pawlak’s Many Valued Information System (MVIS), Non-deterministic Information System (NIS), and related new topics on information incompleteness toward the actual application. Pawlak proposed rough sets, which were originally defined in a standard table, however his research in non-standard tables like MVIS and NIS is also seen. Since rough sets have been known to many researchers deeply and several software tools have been proposed until now, it will be necessary to advance from this research on a standard table to research on MVIS and NIS, especially in regards to NIS. In this chapter, previous research is surveyed and new topics toward the actual application of NIS are proposed, namely data mining under various types of uncertainty, rough set-based estimation of an actual value, machine learning by rule generation, information dilution, and an application to privacy-preserving questionnaire, in NIS. Such new topics will further extend the role of Pawlak’s rough sets.

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References

  1. Aldrich, J.: R. A. Fisher and the making of maximum likelihood 1912–1922. Stat. Sci. 12(3), 162–176 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  2. Aggarwal, C., Yu, S.: A general survey of privacy-preserving data mining models and algorithms. In: Aggarwal, C., Yu, S. (eds.) Privacy-Preserving Data Mining, Models and Algorithms, pp. 11–52. Springer (2008)

    Google Scholar 

  3. Agrawal, R., Srikant, R.: Fast algorithms for mining association rules in large databases. In: Bocca, J.B., Jarke, M., Zaniolo, C (eds.) Proceedings of VLDB’94, pp. 487–499. Morgan Kaufmann (1994)

    Google Scholar 

  4. Agrawal, R., Mannila, H., Srikant, R., Toivonen, H., Verkamo, A. I.: Fast discovery of association rules. In: Advances in Knowledge Discovery and Data Mining, pp. 307–328. AAAI/MIT Press (1996)

    Google Scholar 

  5. Ciucci, D., Flaminio, T.: Generalized rough approximations in PI 1/2. Int. J. Approximate Reasoning 48(2), 544–558 (2008)

    Article  MATH  Google Scholar 

  6. Codd, E.F.: A relational model of data for large shared data banks. Commun. ACM 13(6), 377–387 (1970)

    Article  MATH  Google Scholar 

  7. Demri, S., Orłowska, E.: Incomplete Information: Structure, Inference. Complexity. An EATCS Series, Springer, Monographs in Theoretical Computer Science (2002)

    Book  MATH  Google Scholar 

  8. Frank, A., Asuncion, A.: UCI machine learning repository. Irvine, CA: University of California, School of Information and Computer Science. http://mlearn.ics.uci.edu/MLRepository.html (2010)

  9. Greco, S., Matarazzo, B., Słowiński, R.: Granular computing and data mining for ordered data: The dominance-based rough set approach. In: R.A. Meyers (ed.) Encyclopedia of Complexity and Systems Science, pp. 4283–4305. Springer (2009)

    Google Scholar 

  10. Grzymała-Busse, J. W., Werbrouck, P.: On the best search method in the LEM1 and LEM2 algorithms. In: E. Orłowska (ed.) Incomplete Information: Rough Set Analysis, Studies in Fuzziness and Soft Computing, vol. 13, pp. 75–91. Springer (1998)

    Google Scholar 

  11. Grzymała-Busse, J.W.: Data with missing attribute values: Generalization of indiscernibility relation and rule induction. Trans. Rough Sets 1, 78–95 (2004)

    MATH  Google Scholar 

  12. Grzymała-Busse, J., Rząsa, W.: A local version of the MLEM2 algorithm for rule induction. Fundamenta Informaticae 100, 99–116 (2010)

    MathSciNet  MATH  Google Scholar 

  13. Inuiguchi, M., Yoshioka, Y., Kusunoki, Y.: Variable-precision dominance-based rough set approach and attribute reduction. Int. J. Approximate Reasoning 50(8), 1199–1214 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  14. Komorowski, J., Pawłak, Z., Polkowski, L., Skowron, A.: Rough sets: a tutorial, In: Pal, S. K., Skowron, A. (eds.) Rough Fuzzy Hybridization: A New Method for Decision Making, pp. 3–98. Springer (1999)

    Google Scholar 

  15. Kripke, S.A.: Semantical considerations on modal logic. Acta Philosophica Fennica 16, 83–94 (1963)

    MathSciNet  MATH  Google Scholar 

  16. Kryszkiewicz, M.: Rough set approach to incomplete information systems. Inf. Sci. 112(1–4), 39–49 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  17. Kryszkiewicz, M.: Rules in incomplete information systems. Inf. Sci. 113(3–4), 271–292 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  18. Lipski, W.: On semantic issues connected with incomplete information databases. ACM Trans Database Syst. 4(3), 262–296 (1979)

    Article  Google Scholar 

  19. Lipski, W.: On databases with incomplete information. J. ACM 28(1), 41–70 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  20. Marek, W., Pawłak, Z.: Information storage and retrieval systems: Mathematical foundations. Theor. Comput. Sci. 1(4), 331–354 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  21. Nakata, M., Sakai, H.: Lower and upper approximations in data tables containing possibilistic information. Trans. Rough Sets 7, 170–189 (2007)

    MathSciNet  MATH  Google Scholar 

  22. Nakata, M., Sakai, H.: Applying rough sets to information tables containing possibilistic values. Trans. Comput. Sci. 2, 180–204 (2008)

    MATH  Google Scholar 

  23. Nakata, M., Sakai, H.: Twofold rough approximations under incomplete information. Int. J. Gen. Syst. 42(6), 546–571 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  24. Orłowska, E., Pawłak, Z.: Representation of nondeterministic information. Theoret. Comput. Sci. 29(1–2), 27–39 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  25. Orłowska, E.: Introduction: What you always wanted to know about rough sets, In: Orłowska, E (ed.) Incomplete Information: Rough Set Analysis, Studies in Fuzziness and Soft Computing, vol. 13, pp. 1–20. Springer (1998)

    Google Scholar 

  26. Pawłak, Z.: Information systems theoretical foundations. Inf. Syst. 6(3), 205–218 (1981)

    Article  MATH  Google Scholar 

  27. Pawłak, Z.: Systemy Informacyjne: Podstawy Teoretyczne (In Polish), p. 186. WNT Press (1983)

    Google Scholar 

  28. Pawłak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data, p. 229. Kluwer Academic Publishers (1991)

    Google Scholar 

  29. Pawłak, Z.: Some issues on rough sets. Trans. Rough Sets 1, 1–58 (2004)

    MATH  Google Scholar 

  30. Polkowski, L., Skowron, A. (Eds.): Rough sets in knowledge discovery 1: Methodology and applications. In: Studies in Fuzziness and Soft Computing, vol. 18, p. 576. Springer (1998)

    Google Scholar 

  31. Qian, Y.H., Liang, J.Y., Yao, Y.Y., Dang, C.Y.: MGRS: A multi-granulation rough set. Inf. Sci. 180, 949–970 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  32. Sakai, H., Okuma, A.: Basic algorithms and tools for rough non-deterministic information analysis. Trans. Rough Sets 1, 209–231 (2004)

    MATH  Google Scholar 

  33. Sakai, H., Ishibashi, R., Koba, K., Nakata, M.: Rules and apriori algorithm in non-deterministic information systems. Trans. Rough Sets 9, 328–350 (2008)

    MATH  Google Scholar 

  34. Sakai, H., Wu, M., Yamaguchi, N., Nakata, M.: Rough set-based information dilution by non-deterministic information. In: Ciucci, Davide, et al. (eds.) Proceedings of RSFDGrC2013, vol. 8170, pp. 55–66. Springer, LNCS (2013)

    Google Scholar 

  35. Sakai, H., Wu, M., Yamaguchi, N., Nakata, M.: Non-deterministic information in rough sets: A survey and perspective. In: Pawan Lingras et al. (eds.) Proceedings of RSKT2013 vol. 8171, pp. 7–15. LNCS, Springer (2013)

    Google Scholar 

  36. Sakai, H., Wu, M., Nakata, M.: Apriori-based rule generation in incomplete information databases and non-deterministic information systems. Fundamenta Informaticae 130(3), 343–376 (2014)

    MathSciNet  MATH  Google Scholar 

  37. Sakai, H., Wu M.: The completeness of NIS-Apriori algorithm and a software tool getRNIA. In: Mori, M. (ed.) Proceedings of International Conference on AAI2014, pp. 115–121. IEEE (2014)

    Google Scholar 

  38. Sakai, H., Liu, C.: A consideration on learning by rule generation from tables with missing values. In: Mine, T. (ed.) Proceedings of International Conference on AAI2015, pp. 183–188. IEEE (2015)

    Google Scholar 

  39. Sakai, H., Liu, C., Nakata, M., Tsumoto, S.: A proposal of the privacy-preserving questionnaire by non-deterministic information and its analysis. In: Proceedings of IEEE International Conference on Big Data, pp. 1956–1965 (2016)

    Google Scholar 

  40. Sakai, H.: Execution logs by RNIA software tools. http://www.mns.kyutech.ac.jp/~sakai/RNIA (2016)

  41. Skowron, A., Rauszer, C.: The discernibility matrices and functions in information systems. In: Słowiński, R. (ed.) Intelligent Decision Support—Handbook of Advances and Applications of the Rough Set Theory, pp. 331–362. Kluwer Academic Publishers (1992)

    Google Scholar 

  42. Ślęzak, D., Sakai, H.: Automatic extraction of decision rules from non-deterministic data systems: Theoretical foundations and SQL-based implementation. In: Ślęzak, D., Kim, T.H., Zhang, Y., Ma, J., Chung, K.I. (eds.) Database Theory and Application, Communications in Computer and Information Science, vol. 64, pp. 151–162. Springer (2009)

    Google Scholar 

  43. Tsumoto, S.: Knowledge discovery in clinical databases and evaluation of discovered knowledge in outpatient clinic. Inf. Sci. 124(1–4), 125–137 (2000)

    Article  Google Scholar 

  44. Tsumoto, S.: Automated extraction of hierarchical decision rules from clinical databases using rough set model. Expert Syst. Appl. 24, 189–197 (2003)

    Article  Google Scholar 

  45. Wikipedia: Constraint satisfaction problem. https://en.wikipedia.org/wiki/Constraint_satisfaction_problem

  46. Yao, Y.Y.: A note on definability and approximations. Trans. Rough Sets 7, 274–282 (2007)

    MathSciNet  MATH  Google Scholar 

  47. Yao, Y.Y.: Three-way decisions with probabilistic rough sets. Inf. Sci. 180, 314–353 (2010)

    Article  MathSciNet  Google Scholar 

  48. Yao, Y.Y.: Two sides of the theory of rough sets. Knowl. Based Syst. 80, 67–77 (2015)

    Article  Google Scholar 

  49. Yao, Y.Y., She, Y.: Rough set models in multigranulation spaces. Inform. Sci. 327, 40–56 (2016)

    Article  MathSciNet  Google Scholar 

  50. Zhu, W.: Topological approaches to covering rough sets. Inform. Sci. 177(6), 1499–1508 (2007)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The first author is grateful to Prof. Shusaku Tsumoto for his comments on the privacy-preserving questionnaire. He also thanks Prof. Dominik Ślęzak for his guidance on SQL. This work is supported by JSPS (Japan Society for the Promotion of Science) KAKENHI Grant Number 26330277.

Author information

Authors and Affiliations

  1. Department of Mathematical Science, Kyushu Institute of Technology, Sensui 1-1, Tobata, Kitakyushu, 804-8550, Japan

    Hiroshi Sakai

  2. Faculty of Management and Information Science, Josai International University, Gumyo, Togane, Chiba, 283-0002, Japan

    Michinori Nakata

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

    Yiyu Yao

Authors
  1. Hiroshi Sakai
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  2. Michinori Nakata
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  3. Yiyu Yao
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Corresponding author

Correspondence to Hiroshi Sakai .

Editor information

Editors and Affiliations

  1. Chongqing Key Laboratory of Computational Intelligence, Chongqing University of Posts and Telecommunications, Chongqing, China

    Guoyin Wang

  2. Institute of Mathematics, University of Warsaw Institute of Mathematics, Warsaw, Poland

    Andrzej Skowron

  3. University of Regina, Department of Computer Science University of Regina, Regina, Saskatchewan, Canada

    Yiyu Yao

  4. Institute of Informatics, University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  5. Polish-Japanese Academy IT , Warsaw, Poland

    Lech Polkowski

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Sakai, H., Nakata, M., Yao, Y. (2017). Pawlak’s Many Valued Information System, Non-deterministic Information System, and a Proposal of New Topics on Information Incompleteness Toward the Actual Application. In: Wang, G., Skowron, A., Yao, Y., Ślęzak, D., Polkowski, L. (eds) Thriving Rough Sets. Studies in Computational Intelligence, vol 708. Springer, Cham. https://doi.org/10.1007/978-3-319-54966-8_9

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  • DOI: https://doi.org/10.1007/978-3-319-54966-8_9

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-54966-8

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