Skip to main content
SpringerLink
Log in

Determining Three-Way Decision Regions by Combining Gini Objective Functions and GTRS

  • Conference paper
  • First Online:
Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9437))

Abstract

Game-theoretic rough set model (GTRS) is a recent advancement in determining decision regions by formulating competition or cooperation between multiple measures of decision regions. Different competitions can be formulated with GTRS to gain optimal and balanced decision regions. In three-way decisions, there are some remaining issues where GTRS may be employed to reach a compromise between conflicting measures. When Gini coefficient is used to measure impurity of decision regions, Gini objective functions may be formulated to optimize impurities of multiple decision regions. We aim to examine the problem of minimizing the impurities of immediate and non-commitment decision regions simultaneously. In particular, we consider using GTRS to determine three-way decision regions by finding a solution to Gini objective functions. A compromise solution from various Pareto optimal strategies is obtained with GTRS. The game formulation, Pareto optimal strategies, Nash equilibrium of games, as well as iteration learning mechanism are investigated in detail. An example to demonstrate that compromise decision regions can be obtained by using GTRS to formulate competitions between decision regions is presented.

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

Access this chapter

Log in via an institution

Institutional subscriptions

References

  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)

    Chapter  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  3. Deng, X.F., Yao, Y.Y.: A multifaceted analysis of probabilistic three-way decisions. Fundamenta Informaticae 132(3), 291–313 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  4. Herbert, J.P., Yao, J.T.: Criteria for choosing a rough set model. Comput. Math. Appl. 57(6), 908–918 (2009)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  6. Leyton-Brown, K., Shoham, Y.: Essentials of game theory: a concise multidisciplinary introduction. Synth. Lect. Artif. Intell. Mach. Learn. 2(1), 1–88 (2008)

    MATH  Google Scholar 

  7. Li, H.X., Zhang, L., Huang, B., Zhou, X.Z.: Sequential three-way decision and granulation for cost-sensitive face recognition. Knowledge-Based Systems (2015). http://dx.doi.org/10.1016/j.knosys.2015.07.040

  8. Liu, D., Liang, D.C., Wang, C.C.: A novel three-way decision model based on incomplete information system. Knowledge-Based Systems (2015). http://dx.doi.org/10.1016/j.knosys.2015.07.036

  9. Marler, R.T., Arora, J.S.: Survey of multi-objective optimization methods for engineering. Struct. Multi. Optim. 26(6), 369–395 (2004)

    Article  MathSciNet  MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

  11. Turocy, T., Von Stengel, B.: Game theory. Encycl. Inf. Syst. 2, 403–420 (2002)

    Google Scholar 

  12. Vincent, T.L.: Game theory as a design tool. J. Mech. Design 105(2), 165–170 (1983)

    MathSciNet  Google Scholar 

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

    Google Scholar 

  14. Yao, Y.Y.: Decision-theoretic rough set models. In: Yao, J.T., Lingras, P., Wu, W.-Z., Szczuka, M.S., Cercone, N.J., Ślȩzak, D. (eds.) RSKT 2007. LNCS (LNAI), vol. 4481, pp. 1–12. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  16. Yao, Y.Y.: An outline of a theory of three-way decisions. In: Yao, J.T., 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 

  17. Zhang, Y., Yao, J.T.: Rule measures tradeoff using game-theoretic rough sets. In: Zanzotto, F.M., Tsumoto, S., Taatgen, N., Yao, Y. (eds.) BI 2012. LNCS, vol. 7670, pp. 348–359. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  18. Zhang, Y., Yao, J.T.: Determining three-way decision regions with gini coefficients. In: Cornelis, C., Kryszkiewicz, M., Ślȩzak, D., Ruiz, E.M., Bello, R., Shang, L. (eds.) RSCTC 2014. LNCS, vol. 8536, pp. 160–171. Springer, Heidelberg (2014)

    Google Scholar 

  19. Zhang, Y., Yao, J.T.: Gini objective functions for three-way decisions (manuscript)

    Google Scholar 

Download references

Acknowledgements

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

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Regina, Regina, SK, S4S 0A2, Canada

    Yan Zhang & JingTao Yao

Authors
  1. Yan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. JingTao Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yan Zhang .

Editor information

Editors and Affiliations

  1. University of Regina, Regina, SK, Canada

    Yiyu Yao

  2. Tianjin University, Tianjin, China

    Qinghua Hu

  3. Chongqing University of Posts and Telecommunications, Chongqing, China

    Hong Yu

  4. University of Kansas, Lawrence, KS, USA

    Jerzy W. Grzymala-Busse

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Zhang, Y., Yao, J. (2015). Determining Three-Way Decision Regions by Combining Gini Objective Functions and GTRS. In: Yao, Y., Hu, Q., Yu, H., Grzymala-Busse, J.W. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. Lecture Notes in Computer Science(), vol 9437. Springer, Cham. https://doi.org/10.1007/978-3-319-25783-9_37

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-25783-9_37

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25782-2

  • Online ISBN: 978-3-319-25783-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation