Skip to main content
SpringerLink
Log in

Evidential Probabilities for Rough Set in a Case of Competitiveness

  • Conference paper
Knowledge and Systems Engineering

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 326))

Abstract

Probabilistic rough set based on statistics and equivalence relations can provide membership, boundary approximations, subsets dependency, criterion dependency, three-way decision, and so forth. However, the probability is non-determinant due to randomness and users choices which is subjective in most cases. This research aims to provide determinant probabilities through relevant evidences on three-way decision, called evidential probabilities for rough set (EPRS) to consider the subjective criteria. In this article a research position highlights the boundary regions in terms of subjective criteria showing how subjective criteria may provide a means to narrow the uncertainty by projecting the boundary regions through user preferences in providing better decision precisions. The idea is also projected on prospect theory by showing the adaptable tuning of reference point through decision based subjective preferences. A case study about nations competitiveness is estimated through EPRS and shows the evidential probability can be identified in reality.

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 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
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. Pawlak, Z., Wong, S.K.M., Ziarko, W.: Rough sets: probabilistic versus deterministic approach. International Journal of Man-Machine Studies 29(1), 81–95 (1988)

    Article  MATH  Google Scholar 

  2. Yao, Y.: Probabilistic approaches to rough sets. Expert Systems 20(5), 287–297 (2003)

    Article  Google Scholar 

  3. Yao, Y.: Probabilistic rough set approximations. Int. J. Approx. Reasoning 49(2), 255–271 (2008)

    Article  MATH  Google Scholar 

  4. Ziarko, W.: Probabilistic approach to rough sets. Int. J. Approx. Reasoning 49(2), 272–284 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  5. Yao, Y.: Three-way decisions with probabilistic rough sets. Inf. Sci. 180(3), 341–353 (2010)

    Article  Google Scholar 

  6. Williamson, J., Wheeler, G.: Evidential Probability and Objective Bayesian Epistemology. In: Bandyopadhyay, P.S., Forster, M. (eds.) Handbook of the Philosophy of Statistics. Elsevier (2011)

    Google Scholar 

  7. Yao, Y.: The superiority of three-way decisions in probabilistic rough set models. Inf. Sci. 181(6), 1080–1096 (2011)

    Article  MATH  Google Scholar 

  8. Yang, T.-J., Yao, X.-P., Li, Y.Y.: An axiomatic characterization of probabilistic rough sets. Inf. Sci. 55(1), 130–141 (2014)

    Google Scholar 

  9. Blaszczynski, J., Greco, S., Slowinski, R.: Multi-criteria classification - a new scheme for application of dominance-based decision rules. European Journal of Operational Research 181(3), 1030–1044 (2007)

    Article  MATH  Google Scholar 

  10. Greco, S., Matarazzo, B., Slowinski, R.: Parameterized rough set model using rough membership and bayesian confirmation measures. Int. J. Approx. Reasoning 49(2), 285–300 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  11. Deng, X., Yao, Y.: Decision-theoretic three-way approximations of fuzzy sets. Inf. Sci. 279, 702–715 (2014)

    Article  MathSciNet  Google Scholar 

  12. Liang, D., Liu, D.: Systematic studies on three-way decisions with interval-valued decision-theoretic rough sets. Inf. Sci. 276, 186–203 (2014)

    Article  Google Scholar 

  13. Hu, B.Q.: Three-way decisions space and three-way decisions. Inf. Sci. 281, 21–52 (2014)

    Article  Google Scholar 

  14. Ciucci, D., Dubois, D.: Truth-functionality, rough sets and three-valued logics. In: ISMVL, pp. 98–103. IEEE Computer Society (2010)

    Google Scholar 

  15. Algebras, S., Walker, E.A.: Conditional events, and three-valued logic. IEEE Transaction of Systems, 1699–1707 (1994)

    Google Scholar 

  16. Pedrycz, W.: From fuzzy sets to shadowed sets: Interpretation and computing. Int. J. Intell. Syst. 24(1), 48–61 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  17. Yao, Y.: Interval sets and interval-set algebras. In: IEEE ICCI, pp. 307–314 (2009)

    Google Scholar 

  18. Yao, Y.: An outline of a theory of three-way decisions. In: Yao, J., Yang, Y., Słowiński, R., Greco, S., Li, H., Mitra, S., Polkowski, L. (eds.) RSCTC 2012. LNCS, vol. 7413, pp. 1–17. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  19. Yao, Y.Y., Wong, S.K.M., Lingras, P.: A decision-theoretic rough set model. In: Ras, Z.W., Zemankova, M., Emrich, M.L. (eds.) Methodologies for Intelligent Systems, 5: Proc. of the Fifth International Symposium on Methodologies for Intelligent Systems, pp. 17–24. North-Holland, New York (1990)

    Google Scholar 

  20. Tversky, D., Kahneman, D.: A Prospect theory: An analysis of decision under risk. Econometrica 47, 263–292 (1979)

    Article  MATH  Google Scholar 

  21. Ciucci, D., Dubois, D.: A map of dependencies among three-valued logics. Inf. Sci. 250, 162–177 (2013)

    Article  MathSciNet  Google Scholar 

  22. Arkes, H.R., Hirshleifer, D., Jiang, D., Sonya Lim, S.: Reference point adaptation: Tests in the domain of security trading. Organizational Behavior and Human Decision Processes 105, 67–81 (2008)

    Article  Google Scholar 

  23. Fan, Z.-P., Zhang, X., Chen, F.-D., Liu, Y.: Multiple attribute decision making considering aspiration-levels: A method based on prospect theory. Computers & Industrial Engineering 65(2), 341–350 (2013)

    Article  Google Scholar 

  24. Fujita, H., Ko, Y.-C.: Subjective weights based meta-learning in multi-criteria decision making. In: Fodor, J., Fullér, R. (eds.) Advances in Soft Computing, Intelligent Robotics and Control. Topics in Intelligent Engineering and Informatics, vol. 8. Springer International Publishing (2014)

    Google Scholar 

  25. Lima, M.M.P.P., Gomes, L.F.A.M.: Todim: Basics and application to multicriteria rank-ing of projects with environmental impacts. Foundations of Computing and Decision Sciencesg 16, 113–127 (1992)

    Google Scholar 

  26. Ko, Y.-C., Fujita, H., Tzeng, G.-H.: A simple utility function with the rules-verified weights for analyzing the top competitiveness of wcy 2012. Knowl.-Based Syst. 58, 58–65 (2013)

    Article  Google Scholar 

  27. IMD. World Competitiveness Yearbook. Institute Management Development, Lausanne, Switzerland (2012), http://worldcompetitiveness.com/OnLine/App/Index.htm

  28. Pawlak, Z.: Rough set approach to knowledge-based decision support. European Journal of Operational Research 99(1), 48–57 (1997)

    Article  MATH  Google Scholar 

  29. Greco, S., Matarazzo, B., Slowinski, R.: Rough sets theory for multicriteria decision analysis. European Journal of Operational Research 129(1), 1–47 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  30. Pawlak, Z.: Rough sets, decision algorithms and bayes’ theorem. European Journal of Operational Research 136(1), 181–189 (2002)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Software and Information Science, Iwate Prefectural University, Takizawa, Japan

    Hamido Fujita

  2. Department of Information Management, Chung Hua University, Hsinchu, Taiwan

    Yu-Chien Ko

Authors
  1. Hamido Fujita
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu-Chien Ko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hamido Fujita .

Editor information

Editors and Affiliations

  1. Faculty of Information Technology, VNU University of Engineering and Technology, Hanoi, Vietnam

    Viet-Ha Nguyen

  2. Faculty of Information Technology, VNU University of Engineering and Technology, Hanoi, Vietnam

    Anh-Cuong Le

  3. School of Knowledge Science, Japan Advanced Institute of Science and Technology, Nomi, Ishikawa, Japan

    Van-Nam Huynh

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Fujita, H., Ko, YC. (2015). Evidential Probabilities for Rough Set in a Case of Competitiveness. In: Nguyen, VH., Le, AC., Huynh, VN. (eds) Knowledge and Systems Engineering. Advances in Intelligent Systems and Computing, vol 326. Springer, Cham. https://doi.org/10.1007/978-3-319-11680-8_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-11680-8_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11679-2

  • Online ISBN: 978-3-319-11680-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation