Skip to main content
SpringerLink
Log in

Probabilistic Approaches to the Rough Set Theory and Their Applications in Decision-Making

  • Chapter
Soft Computing for Business Intelligence

Part of the book series: Studies in Computational Intelligence ((SCI,volume 537))

Abstract

Rough sets were presented by Professor Zdzislaw Pawlak in a seminal paper published in 1982. Rough Sets Theory (RST) has evolved into a methodology for dealing with different types of problems, such as the uncertainty produced by inconsistencies in data. RST is the best tool for modeling uncertainty when it shows up as inconsistency, according to several analyses. This is the main reason for which the RST has been included in the family of Soft Computing techniques. The classical RST is defined by using an equivalence relation as an indiscernibility relation. This is very restrictive in different domains, so several extensions of the theory have been formulated. One of these alternatives is based on a probabilistic approach, where several variants have been proposed such as the Variable Precision Rough Sets model, Rough Bayesian model, and Parameterized Rough Set model. Here is presented an analysis about the evolution of the RST in order to enrich the applicability to solve real problems by means of the probabilistic approaches of rough sets and its application to knowledge discovering and decision making, two main activities in Business Intelligence.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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. An, A., et al.: Discovering rules for water demand prediction: an enhanced rough-set approach. Engineering Applications in Artificial Intelligence 9(6), 645–653 (1996)

    Article  Google Scholar 

  2. Bello PĂ©rez, R., Verdegay Galdeano, J.L.: On Hybridizations in Soft Computing: Rough Sets and Metaheuristics. In: Proceeding of World Conference on SoftComputing, San Francisco, USA, May 23-26 (2011)

    Google Scholar 

  3. Bello Pérez, R., Verdegay Galdeano, J.L.: Rough sets in the Soft Computing environment. Information Sciences 212, 1–14 (2012)

    Article  MathSciNet  Google Scholar 

  4. Beynon, M.J.: An investigation of β-reduct selection within the variable precision rough sets model. In: Ziarko, W.P., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 114–122. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  5. Beynon, M.: Reducts within the variable precision rough sets models: a further investigation. European Journal of Operational Research 134, 592–605 (2001)

    Article  MATH  Google Scholar 

  6. Bonnissone, P.P., Tong, R.M.: Editorial: Reasoning with uncertainty in expert systems. Int. J. Man Machine Studies 22, 241–250 (1985)

    Article  Google Scholar 

  7. Bonissone, P.P.: Soft Computing: the Convergence of Emerging Reasoning Technologies. Journal of Soft Computing 1(1), 6–18 (1997)

    Article  MathSciNet  Google Scholar 

  8. Bosc, P., Prade, H.: An introduction to fuzzy set and possibility theory based approaches to the treatment of uncertainty and imprecision in database management systems. In: Proc. of Second Workshop Uncertainty management in Information Systems: from Needs to Solutions, California (1993)

    Google Scholar 

  9. Dun, L., Huaxiong, L., Xianzhong, Z.: Two Decades’ Research on Decision-theoretic Rough Sets. In: Proceedings of the 9th IEEE International Conference on Cognitive Informatics, ICCI 2010, article number 5599770, pp. 968–973 (2010)

    Google Scholar 

  10. Greco, S., Matarazzo, B., Slowinski, R.: Parameterized rough set model using rough membership and Bayesian confirmation measures. International Journal of Approximate Reasoning 49, 285–300 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  11. Grzymala-Busse, J.W.: Managing uncertainty in machine learning from examples. In: Proceedings of the Workshop Intelligent Information Systems III, Poland, June 6-10, pp. 6–10 (1994)

    Google Scholar 

  12. Herbert, J., Yao, J.: Criteria for choosing a rough set model. Computers and Mathematics with Applications 57, 908–918 (2009)

    Article  MATH  Google Scholar 

  13. Jang, J.R., et al.: Neuro-Fuzzy and Soft Computing: a computational approach to learning and machine intelligence. Prentice Hall (1997)

    Google Scholar 

  14. Jia, X., Li, W., Shang, L., Chen, J.: An Optimization Viewpoint of Decision-Theoretic Rough Set Model. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 457–465. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  15. Jun-hua, H., Xiao-hong, C.: Multi-criteria decision making method based on dominance relation and variable precision rough set. Systems Engineering and Electronics 32(4), 759–763 (2010)

    Google Scholar 

  16. Li, R., Zhao, Y., Zhang, F., Song, L.: Rough Sets in Hybrid Soft Computing Systems. In: Alhajj, R., Gao, H., Li, X., Li, J., Zaïane, O.R. (eds.) ADMA 2007. LNCS (LNAI), vol. 4632, pp. 35–44. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  17. Liu, D., Li, T., Liang, D.: A New Discriminant Analysis Approach under Decision-Theoretic Rough Sets. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 476–485. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  18. Ming-li, H., Fei-fei, S., Ya-huan, C.: A multi-attribute decision analysis method based on rough sets dealing with uncertain information. In: Proceedings of 2011 IEEE International Conference on Grey Systems and Intelligent Services, GSIS 2011, art. no. 6043984, pp. 576–581 (2011)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  20. 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 

  21. Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Boston (1991)

    Book  MATH  Google Scholar 

  22. Parsons, S.: Current approaches to handling imperfect information in data and knowledge bases. IEEE Trans. on Knowledge and Data Engineering 8(3) (June 1996)

    Google Scholar 

  23. Ramanathan, G.: Group preference aggregation methods employed in AHP: an evaluation and an intrinsic process for deriving members’ weightages. European Journal on Operation Research 79, 249–265 (1994)

    Article  MATH  Google Scholar 

  24. Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27(2-3), 245–253 (1996)

    MATH  MathSciNet  Google Scholar 

  25. Ślęzak, D.: Rough sets and Bayes factor. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets III. LNCS, vol. 3400, pp. 202–229. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  26. Slowinski, R., Vanderpooten, D.: Similarity relation as a basis for rough approximations. Advances in Machine Intelligence & Soft-Computing IV, 17–33

    Google Scholar 

  27. Su, C.T., Hsu, J.H.: Precision parameter in the variable precision rough set model: an application. Omega 34, 149–157 (2006)

    Article  Google Scholar 

  28. Tay, F.E., Shen, L.: Economic and financial prediction using rough set model. European Journal of Operational Research 141, 641–659 (2002)

    Article  MATH  Google Scholar 

  29. Verdegay, J.L., Yager, R.R., Bonissone, P.P.: On heuristics as a fundamental constituent of soft computing. Fuzzy Sets and Systems 159, 846–855 (2008)

    Article  MathSciNet  Google Scholar 

  30. Wong, S.K.M., Ziarko, W.: Comparison of the probabilistic approximate classification and the fuzzy set model. Fuzzy Sets and Systems 21, 357–362 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  31. Xie, G., Zhang, J., Lai, K.K., Yu, L.: Variable precision rough set for group decision-making: An application. International Journal of Approximate Reasoning 49, 331–343 (2008)

    Article  MATH  Google Scholar 

  32. Yao, Y.Y.: Probabilistic Approaches to Rough Sets. Expert Systems 20(5), 287–297 (2003)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  34. Yao, Y.: Three-way decision: an interpretation of rules in rough set theory. In: Wen, P., Li, Y., Polkowski, L., Yao, Y., Tsumoto, S., Wang, G. (eds.) RSKT 2009. LNCS (LNAI), vol. 5589, pp. 642–649. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  35. Yao, Y.Y.: Three-way decisions with probabilistic rough sets. Information Sciences 180, 341–353 (2010)

    Article  MathSciNet  Google Scholar 

  36. Yao, Y.Y.: The superiority of three-way decision in probabilistic rough set models. Information Sciences 181, 1080–1096 (2011)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  38. Yao, Y.Y., Wong, S.K.M., Lin, T.Y.: A review of rough set models. In: Lin, T.Y., Cercone, N. (eds.) Rough Sets and Data Mining: Analysis for Imprecise Data, pp. 47–75. Kluwer Academic Publishers, Boston (1997)

    Chapter  Google Scholar 

  39. Yang, X., Song, H., Li, T.-J.: Decision Making in Incomplete Information System Based on Decision-Theoretic Rough Sets. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 495–503. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  40. Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  41. Zhou, X., Li, H.: A Multi-View Decision Model Based on Decision-Theoretic Rough Set. In: Wen, P., Li, Y., Polkowski, L., Yao, Y., Tsumoto, S., Wang, G. (eds.) RSKT 2009. LNCS, vol. 5589, pp. 650–657. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  42. Zhou, B.: A New Formulation of Multi-category Decision-Theoretic Rough Sets. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 514–522. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  43. Ziarko, W.: Variable precision Rough sets model. Journal of Computer and System Science 46(1), 39–59 (1993)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Central University of Las Villas, Santa Clara, Cuba

    Rafael Bello Pérez & Maria M. Garcia

Authors
  1. Rafael Bello PĂ©rez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Maria M. Garcia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rafael Bello PĂ©rez .

Editor information

Editors and Affiliations

  1. Centro de Estudios de Técnicas de Dirección, Instituto Superior Politécnico José Antonio Echeverría, La Habana, Cuba

    Rafael Espin

  2. Centro de Estudios de Informática Carretera a Camajuani, Universidad Central Marta Abreu de Las Villas, Santa Clara, Cuba

    Rafael Bello PĂ©rez

  3. Department of Applied Mathematics and Computer Science, Universidad de Cantabria, Santander, Spain

    Angel Cobo

  4. Department für Informatik, Carl Von Ossietzky Universität Oldenburg, Oldenburg, Germany

    Jorge Marx

  5. Instituto Superior Politécnico José Antonio Echeverría, La Habana, Cuba

    Ariel Racet Valdés

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Pérez, R.B., Garcia, M.M. (2014). Probabilistic Approaches to the Rough Set Theory and Their Applications in Decision-Making. In: Espin, R., Pérez, R., Cobo, A., Marx, J., Valdés, A. (eds) Soft Computing for Business Intelligence. Studies in Computational Intelligence, vol 537. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-53737-0_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-53737-0_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-53736-3

  • Online ISBN: 978-3-642-53737-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation