Skip to main content

Towards Coordination Game Formulation in Game-Theoretic Rough Sets

  • 945 Accesses

Part of the Lecture Notes in Computer Science book series (LNAI,volume 9920)


Game-theoretic rough set model (GTRS) is a recent advancement in determining three rough set regions by formulating games between multiple measures. GTRS has been focusing on researching competitive games in which the involved game players have opposite interests or incentives. There are different types of games that can be adopted in GTRS, such as coordination games, cooperation games, as well as competition games. Coordination games are a class of games in which the involved players have harmonious interests and enforce coordinative behaviors to achieve an efficient outcome. In this paper, we formulate coordination games between measures to determine rough set regions. Especially, we analyze the measures for evaluating equivalence classes. We determine rough regions to which every equivalence class should belong to by formulating coordination games and finding equilibrium for each equivalence class. The motivation and process of formulating coordination games are discussed in detail, and a demonstrative example shows the feasibility of the proposed approach.


  • Game-theoretic rough sets
  • Coordination games
  • Rough sets
  • Measures

This is a preview of subscription content, access via your institution.

Buying options

USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and 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

Learn about institutional subscriptions


  1. Azam, N., Yao, J.T.: Multiple criteria decision analysis with game-theoretic rough sets. In: Li, T., Nguyen, H.S., Wang, G., Grzymala-Busse, J., Janicki, R., Hassanien, A.E., Yu, H. (eds.) RSKT 2012. LNCS, vol. 7414, pp. 399–408. Springer, Heidelberg (2012)

    CrossRef  Google Scholar 

  2. Azam, N., Yao, J.T.: Analyzing uncertainties of probabilistic rough set regions with game-theoretic rough sets. Int. J. Approximate Reason. 55(1), 142–155 (2014)

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Ciucci, D.: Attribute dynamics in rough sets. In: International Symposium on Methodologies for Intelligent Systems, pp. 43–51 (2011)

    Google Scholar 

  4. Cooper, R.: Coordination Games. Cambridge University Press, New York (1999)

    CrossRef  MATH  Google Scholar 

  5. Grzymala-Busse, J.W.: Knowledge acquisition under uncertaintya rough set approach. J. intell. Robot. Syst. 1(1), 3–16 (1988)

    CrossRef  MathSciNet  Google Scholar 

  6. Herbert, J.P., Yao, J.T.: Game-theoretic rough sets. Fundamenta Informaticae 108(3–4), 267–286 (2011)

    MathSciNet  MATH  Google Scholar 

  7. Leyton-Brown, K., Shoham, Y.: Essentials of Game Theory: A Concise Multidisciplinary Introduction. Morgan & Claypool Publishers, San Rafael (2008)

    MATH  Google Scholar 

  8. Liang, J.Y., Li, D.Y.: Uncertainty and Knowledge Acquisition in Information Systems. Science Press, Beijing (2005)

    Google Scholar 

  9. Lingras, P., Peters, G.: Applying rough set concepts to clustering. In: Rough Sets: Selected Methods and Applications in Management and Engineering, pp. 23–37. Springer (2012)

    Google Scholar 

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

    CrossRef  MATH  Google Scholar 

  11. Qian, Y.H., Liang, J.Y., Li, D.Y., Zhang, H.Y., Dang, C.Y.: Measures for evaluating the decision performance of a decision table in rough set theory. Inf. Sci. 178(1), 181–202 (2008)

    CrossRef  MATH  Google Scholar 

  12. Yao, J.T., Herbert, J.P.: A game-theoretic perspective on rough set analysis. J. Chongqing Univ. Posts Telecommun. 20(3), 291–298 (2008)

    MathSciNet  Google Scholar 

  13. Yao, J.T., Azam, N.: Web-based medical decision support systems for three-way medical decision making with game-theoretic rough sets. IEEE Trans. Fuzzy Syst. 23(1), 3–15 (2015)

    CrossRef  Google Scholar 

  14. Yao, J.T., Ciucci, D., Zhang, Y.: Generalized rough sets. In: Springer Handbook of Computational Intelligence. Springer, Berlin (2015)

    Google Scholar 

  15. Yao, Y.Y.: Rough sets and three-way decisions. In: Ciucci, D., Mitra, S., Wu, W.-Z. (eds.) RSKT 2015. LNCS, vol. 9436, pp. 62–73. Springer, Heidelberg (2015). doi:10.1007/978-3-319-25754-9_6

    CrossRef  Google Scholar 

  16. Yao, Y.Y., Zhao, Y.: Attribute reduction in decision-theoretic rough set models. Inf. Sci. 178(17), 3356–3373 (2008)

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. Yao, Y.Y.: Probabilistic rough set approximations. Int. J. Approximate Reason. 49(2), 255–271 (2008)

    CrossRef  MATH  Google Scholar 

  18. Zhang, Y., Yao, J.T.: Determining three-way decision regions by combining gini objective functions and GTRS. In: Yao, Y., Hu, Q., Yu, H., Grzymala-Busse, J.W. (eds.) RSFDGrC 2015. LNCS, vol. 9437, pp. 414–425. Springer, Heidelberg (2015). doi:10.1007/978-3-319-25783-9_37

    CrossRef  Google Scholar 

Download references


This work is partially supported by a Discovery Grant from NSERC Canada, the University of Regina Gerhard Herzberg Fellowship.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Jing Tao Yao .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2016 Springer International Publishing AG

About this paper

Cite this paper

Zhang, Y., Yao, J.T. (2016). Towards Coordination Game Formulation in Game-Theoretic Rough Sets. In: Flores, V., et al. Rough Sets. IJCRS 2016. Lecture Notes in Computer Science(), vol 9920. Springer, Cham.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-47159-4

  • Online ISBN: 978-3-319-47160-0

  • eBook Packages: Computer ScienceComputer Science (R0)