Skip to main content
SpringerLink
Log in

Generalizations of Approximations

  • Conference paper
Rough Sets and Knowledge Technology (RSKT 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8171))

Included in the following conference series:

Abstract

In this paper we consider a generalization of the indiscernibility relation, i.e., a relation R that is not necessarily reflexive, symmetric, or transitive. There exist 36 basic definitions of lower and upper approximations based on such relation R. Additionally, there are six probabilistic approximations, generalizations of 12 corresponding lower and upper approximations. How to convert remaining 24 lower and upper approximations to 12 respective probabilistic approximations is an open problem.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Clark, P.G., Grzymala-Busse, J.W.: Experiments on probabilistic approximations. In: Proceedings of the 2011 IEEE International Conference on Granular Computing, pp. 144–149 (2011)

    Google Scholar 

  2. Clark, P.G., Grzymala-Busse, J.W.: Experiments on rule induction from incomplete data using three probabilistic approximations. In: Proceedings of the 2012 IEEE International Conference on Granular Computing, pp. 90–95 (2012)

    Google Scholar 

  3. Clark, P.G., Grzymala-Busse, J.W.: Experiments using three probabilistic approximations for rule induction from incomplete data sets. In: Proceeedings of the MCCSIS 2012, IADIS European Conference on Data Mining, ECDM 2012, pp. 72–78 (2012)

    Google Scholar 

  4. Clark, P.G., Grzymala-Busse, J.W.: Rule induction using probabilistic approximations and data with missing attribute values. In: Proceedings of the 15th IASTED International Conference on Artificial Intelligence and Soft Computing, ASC 2012, pp. 235–242 (2012)

    Google Scholar 

  5. Clark, P.G., Grzymala-Busse, J.W., Hippe, Z.S.: How good are probabilistic approximations for rule induction from data with missing attribute values? In: Yao, J., Yang, Y., Słowiński, R., Greco, S., Li, H., Mitra, S., Polkowski, L. (eds.) RSCTC 2012. LNCS, vol. 7413, pp. 46–55. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  6. Clark, P.G., Grzymala-Busse, J.W., Kuehnhausen, M.: Local probabilistic approximations for incomplete data. In: Chen, L., Felfernig, A., Liu, J., Raś, Z.W. (eds.) ISMIS 2012. LNCS, vol. 7661, pp. 93–98. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  7. Clark, P.G., Grzymala-Busse, J.W., Kuehnhausen, M.: Mining incomplete data with many missing attribute values. a comparison of probabilistic and roug set approaches. In: Proceedings of the INTELLI 2013, the Second International Conference on Intelligent Systems and Applications, pp. 12–17 (2013)

    Google Scholar 

  8. Grzymala-Busse, J.W.: Rough set strategies to data with missing attribute values. In: Workshop Notes, Foundations and New Directions of Data Mining, in Conjunction with the 3rd International Conference on Data Mining, pp. 56–63 (2003)

    Google Scholar 

  9. Grzymala-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., Swiniarski, R.W., Szczuka, M.S. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 78–95. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  10. Grzymala-Busse, J.W.: Three approaches to missing attribute values—a rough set perspective. In: Proceedings of the Workshop on Foundation of Data Mining, in conjunction with the Fourth IEEE International Conference on Data Mining, pp. 55–62 (2004)

    Google Scholar 

  11. Grzymala-Busse, J.W.: Generalized parameterized approximations. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 136–145. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  12. Grzymala-Busse, J.W., Marepally, S.R., Yao, Y.: An empirical comparison of rule sets induced by LERS and probabilistic rough classification. In: Szczuka, M., Kryszkiewicz, M., Ramanna, S., Jensen, R., Hu, Q. (eds.) RSCTC 2010. LNCS, vol. 6086, pp. 590–599. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  13. Grzymala-Busse, J.W., Rząsa, 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 

  14. Grzymala-Busse, J.W., Rząsa, W.: Definability of approximations for a generalization of the indiscernibility relation. In: Proceedings of the 2007 IEEE Symposium on Foundations of Computational Intelligence (IEEE FOCI 2007), pp. 65–72 (2007)

    Google Scholar 

  15. Grzymala-Busse, J.W., Rząsa, W.: Local and global approximations for incomplete data. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets VIII. LNCS, vol. 5084, pp. 21–34. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  16. Grzymala-Busse, J.W., Rząsa, W.: Definability and other properties of approximations for generalized indiscernibility relations. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets XI. LNCS, vol. 5946, pp. 14–39. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  17. Grzymala-Busse, J.W., Yao, Y.: A comparison of the LERS classification system and rule management in PRSM. In: Chan, C.-C., Grzymala-Busse, J.W., Ziarko, W.P. (eds.) RSCTC 2008. LNCS (LNAI), vol. 5306, pp. 202–210. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  18. Grzymala-Busse, J.W., Yao, Y.: Probabilistic rule induction with the LERS data mining system. International Journal of Intelligent Systems 26, 518–539 (2011)

    Article  Google Scholar 

  19. Grzymala-Busse, J.W., Ziarko, W.: Data mining based on rough sets. In: Wang, J. (ed.) Data Mining: Opportunities and Challenges, pp. 142–173. Idea Group Publ., Hershey (2003)

    Google Scholar 

  20. Kryszkiewicz, M.: Rough set approach to incomplete information systems. In: Proceedings of the Second Annual Joint Conference on Information Sciences, pp. 194–197 (1995)

    Google Scholar 

  21. Kryszkiewicz, M.: Rules in incomplete information systems. Information Sciences 113(3-4), 271–292 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  22. Lin, T.Y.: Neighborhood systems and approximation in database and knowledge base systems. In: Proceedings of the ISMIS 1989, the Fourth International Symposium on Methodologies of Intelligent Systems, pp. 75–86 (1989)

    Google Scholar 

  23. Lin, T.Y.: Topological and fuzzy rough sets. In: Slowinski, R. (ed.) Intelligent Decision Support. Handbook of Applications and Advances of the Rough Sets Theory, pp. 287–304. Kluwer Academic Publishers, Dordrecht (1992)

    Chapter  Google Scholar 

  24. Liu, G., Zhu, W.: Approximations in rough sets vs granluar computing for coverings. International Journal of Cognitive Informatics and Natural Intelligence 4, 63–76 (2010)

    Article  Google Scholar 

  25. Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)

    Article  MathSciNet  MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

  27. Pawlak, Z., Skowron, A.: Rough sets: Some extensions. Information Sciences 177, 28–40 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  28. Pawlak, Z., Wong, S.K.M., Ziarko, W.: Rough sets: probabilistic versus deterministic approach. International Journal of Man-Machine Studies 29, 81–95 (1988)

    Article  MATH  Google Scholar 

  29. Ślęzak, D., Ziarko, W.: The investigation of the bayesian rough set model. International Journal of Approximate Reasoning 40, 81–91 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  30. Slowinski, R., Vanderpooten, D.: A generalized definition of rough approximations based on similarity. IEEE Transactions on Knowledge and Data Engineering 12, 331–336 (2000)

    Article  Google Scholar 

  31. Stefanowski, J.: Algorithms of Decision Rule Induction in Data Mining. Poznan University of Technology Press, Poznan (2001)

    Google Scholar 

  32. 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. 73–82. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  33. Stefanowski, J., Tsoukias, A.: Incomplete information tables and rough classification. Computational Intelligence 17(3), 545–566 (2001)

    Article  Google Scholar 

  34. Tsumoto, S., Tanaka, H.: PRIMEROSE: probabilistic rule induction method based on rough sets and resampling methods. Computational Intelligence 11, 389–405 (1995)

    Article  Google Scholar 

  35. Wang, G.: Extension of rough set under incomplete information systems. In: Proceedings of the IEEE International Conference on Fuzzy Systems, pp. 1098–1103 (2002)

    Google Scholar 

  36. Wong, S.K.M., Ziarko, W.: INFER—an adaptive decision support system based on the probabilistic approximate classification. In: Proceedings of the 6th International Workshop on Expert Systems and their Applications, pp. 713–726 (1986)

    Google Scholar 

  37. Yao, Y.Y.: Two views of the theory of rough sets in finite universes. International Journal of Approximate Reasoning 15, 291–317 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  38. Yao, Y.Y.: Relational interpretations of neighborhood operators and rough set approximation operators. Information Sciences 111, 239–259 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  39. Yao, Y.Y.: Probabilistic approaches to rough sets. Expert Systems 20, 287–297 (2003)

    Article  Google Scholar 

  40. Yao, Y.Y.: Probabilistic rough set approximations. International Journal of Approximate Reasoning 49, 255–271 (2008)

    Article  MATH  Google Scholar 

  41. Yao, Y.Y., Lin, T.Y.: Generalization of rough sets using modal logics. Intelligent Automation and Soft Computing 2, 103–120 (1996)

    Article  Google Scholar 

  42. Yao, Y.Y., Wong, S.K.M.: A decision theoretic framework for approximate concepts. International Journal of Man-Machine Studies 37, 793–809 (1992)

    Article  Google Scholar 

  43. Yao, Y.Y., Wong, S.K.M., Lingras, P.: A decision-theoretic rough set model. In: Proceedings of the 5th International Symposium on Methodologies for Intelligent Systems, pp. 388–395 (1990)

    Google Scholar 

  44. Ziarko, W.: Variable precision rough set model. Journal of Computer and System Sciences 46(1), 39–59 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  45. Ziarko, W.: Probabilistic approach to rough sets. International Journal of Approximate Reasoning 49, 272–284 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, University of Kansas, Lawrence, KS, 66045, USA

    Patrick G. Clark & Jerzy W. Grzymała-Busse

  2. Institute of Computer Science, Polish Academy of Sciences, 01-237, Warsaw, Poland

    Jerzy W. Grzymała-Busse

  3. Department of Computer Science, Rzeszow University, 35-310, Rzeszow, Poland

    Wojciech Rząsa

Authors
  1. Patrick G. Clark
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jerzy W. Grzymała-Busse
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wojciech Rząsa
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Saint Mary’s University, B3H 3C3, Halifax, NS, Canada

    Pawan Lingras

  2. Maria Curie-Skłodowska University, Lublin, Poland

    Marcin Wolski

  3. University of Granada, Spain

    Chris Cornelis

  4. Indian Statistical Institute, 700108, Kolkata, India

    Sushmita Mitra

  5. University of Warsaw, 02-097, Warsaw, Poland

    Piotr Wasilewski

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Clark, P.G., Grzymała-Busse, J.W., Rząsa, W. (2013). Generalizations of Approximations. In: Lingras, P., Wolski, M., Cornelis, C., Mitra, S., Wasilewski, P. (eds) Rough Sets and Knowledge Technology. RSKT 2013. Lecture Notes in Computer Science(), vol 8171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41299-8_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-41299-8_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41298-1

  • Online ISBN: 978-3-642-41299-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation