Skip to main content
SpringerLink
Log in

Cooperative Games with the Intuitionistic Fuzzy Coalitions and Intuitionistic Fuzzy Characteristic Functions

  • Conference paper
  • First Online:
Book cover Game Theory and Applications (China GTA 2016, China-Dutch GTA 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 758))

  • 738 Accesses

Abstract

In this paper, the definition of the Shapley function for intuitionistic fuzzy cooperative games is given by extending the fuzzy cooperative games. Based on the extended Hukuhara difference, the specific expression of the Shapley intuitionistic fuzzy cooperative games with multilinear extension form is obtained, and its existence and uniqueness are discussed. Furthermore, the properties of the Shapley function are researched. Finally, the validity and applicability of the proposed method, as well as comparison analysis with other methods are illustrated with a numerical example.

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 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

Institutional subscriptions

References

  1. Li, D.F.: Fuzzy Multi objective Many-Person Decision Makings and Games. National Defense Industry Press, Beijing (2003)

    Google Scholar 

  2. Owen, G.: Game Theory, 2nd edn. Academic Press, New York (1982)

    MATH  Google Scholar 

  3. Aubin, J.P.: Mathematical Methods of Game and Economic Theory. North-Holland, Amsterdam (1982)

    Google Scholar 

  4. Li, D.F.: An effective methodology for solving matrix games with fuzzy payoffs. IEEE Trans. Cybern. 43(2), 610–621 (2013)

    Article  Google Scholar 

  5. Li, D.F.: Linear programming approach to solve interval-valued matrix games. Journal 39, 655–666 (2011)

    Google Scholar 

  6. Li, D.F.: Models and Methods for Interval-Valued Cooperative Games in Economic Management. Springer, Cham (2016)

    Google Scholar 

  7. Adler, I.: The equivalence of linear programs and zero-sum games. Int. J. Game Theory 42, 165–177 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Butnariu, D.: Fuzzy games: a description of the concept. Fuzzy Sets Syst. 1, 181–192 (1978)

    Google Scholar 

  9. Molina, E., Tejada, J.: The equalizer and the lexicographical solutions for cooperative fuzzy games: characterizations and properties. Fuzzy Sets Syst. 125, 369–387 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  10. Sheremetov, L.B., Cortés, J.C.R.: Fuzzy coalition formation among rational cooperative agents. Journal 2691, 268–280 (2003)

    MATH  Google Scholar 

  11. Butnariu, D., Klement, E.P.: Triangular Norm-Based Measures and Games with Fuzzy Coalitions. Kluwer Academic Publishers, Dordrecht (1993)

    Book  MATH  Google Scholar 

  12. Bumariu, D., Kroupa, T.: Enlarged cores and bargaining schemes in games with fuzzy coalitions. Fuzzy Sets Syst. 160(5), 635–643 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  13. Sakawa, M., Nishizaki, I.: A lexicographical concept in an n-person cooperative fuzzy game. Fuzzy Sets Syst. 61, 265–275 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  14. Dan, B.: Stability and Shapley value for an n-persons fuzzy game. Fuzzy Sets Syst. 4(1), 63–72 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  15. Mareš, M.: Fuzzy coalition structures. Fuzzy Sets Syst. 114(1), 23–33 (2000)

    Article  MATH  Google Scholar 

  16. Yu, X.H., Zhang, Q.: Shapley value for cooperative games with fuzzy coalition. J. Beijing Inst. Technol. 17(2), 249–252 (2008)

    MathSciNet  MATH  Google Scholar 

  17. Radzik, T.: Poor convexity and Nash equilibria in games. Int. J. Game Theory 43, 169–192 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  18. Nishizaki, I., Sakawa, M.: Fuzzy and multiobjective games for conflict resolution. Stud. Fuzziness Soft Comput. 64(6) (2001)

    Google Scholar 

  19. Tsurumi, M., Tanino, T., Inuiguchi, M.: A Shapley function on a class of cooperative fuzzy games. Eur. J. Oper. Res. 129, 596–618 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  20. Mareš, M., Vlach, M.: Linear coalition games and their fuzzy extensions. Int. J. Uncertain Fuzziness Knowl. Based Syst. 9, 341–354 (2001)

    Article  MATH  Google Scholar 

  21. Shapley, L.S.: A value for n-person of games. Ann. Oper. Res. 28, 307–318 (1953)

    Google Scholar 

  22. Banks, H.T., Jacobs, M.Q.: A differential calculus for multifunctions. J. Math. Anal. Appl. 29, 46–272 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  23. Yu, X.H., Zhang, Q.: The fuzzy core in games with fuzzy coalitions. J. Comput. Appl. Math. 230, 173–186 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  24. Meng, F.Y., Zhao, J.X., Zhang, Q.: The Shapley function for fuzzy games with fuzzy characteristic functions. J. Intell. Fuzzy Syst. 25, 23–35 (2003)

    MathSciNet  MATH  Google Scholar 

  25. Meng, F.Y., Jiang, D.M.: Fuzzy games on augmenting systems with fuzzy characteristic functions. J. Intell. Fuzzy Syst. 27, 119–129 (2014)

    MathSciNet  MATH  Google Scholar 

  26. Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  27. Atanassov, K.T.: Intuitionistic Fuzzy Sets. Springer, Heidelberg (1999)

    Book  MATH  Google Scholar 

  28. Li, D.F., Nan, J.X.: Extension of the TOPSIS for multi-attribute group decision making under atanassov IFS environments. Int. J. Fuzzy Syst. Appl. 1(4), 44–58 (2011)

    MathSciNet  Google Scholar 

  29. Li, D.F., Nan, J.X.: An extended weighted average method for MADM using intuitionistic fuzzy sets and sensitivity analysis. Crit. View 5, 5–25 (2011)

    Google Scholar 

  30. Li, D.F.: Extension of the LINMAP for multiattribute decision making under atanassov’s intuitionistic fuzzy environment. Fuzzy Optim. Decis. Making 7(1), 17–34 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  31. Nayak, P.K., Pal, M.: Bi-matrix games with intuitionistic fuzzy goals. Iranian J. Fuzzy Syst. 7(1), 65–79 (2010)

    MathSciNet  MATH  Google Scholar 

  32. Li, D.F., Nan, J.X.: A nonlinear programming approach to matrix games with payoffs of atanassov’s intuitionistic fuzzy sets. Int. J. Uncertainty, Fuzziness Knowl. Based Syst. 17(4), 585–607 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  33. Li, D.F., Yang, J.: A difference-index based ranking bilinear programming approach to solving bi-matrix games with payoffs of trapezoidal intuitionistic fuzzy numbers. J. Appl. Math. 2013(4), 1–10 (2013)

    Google Scholar 

  34. Mielcová, E.: Core of n-person transferable utility games with intuitionistic fuzzy expectations In: Jezic, G., Howlett, R., Jain, L. (eds.) Agent and Multi-Agent Systems: Technologies and Applications. Smart Innovation, Systems and Technologies, vol. 38. Springer, Cham (2015). doi 10.1007/978-3-319-19728-9_14

  35. Li, D.F., Liu, J.C.: A parameterized nonlinear programming approach to solve matrix games with payoffs of I-Fuzzy numbers. IEEE Trans. Fuzzy Syst. 23(4), 885–896 (2015)

    Article  Google Scholar 

  36. Mahapatra, G.S., Roy, T.K.: Intuitionistic fuzzy number and its arithmetic operation with application a system failure. J. Uncertain Syst. 7(2), 92–107 (2013)

    Google Scholar 

  37. Young, H.P.: Monotonic solutions of cooperative games. Int. J. Game Theory 14(2), 65–72 (1985)

    Google Scholar 

Download references

Acknowledgments

This research was sponsored by the National Natural Science Foundation of China (No.71231003), the National Natural Science Foundation of China (Nos. 71561008, 71461005), the Science Foundation of Guangxi Province in China (No. 2014GXNSFAA118010) and the Graduate Education Innovation Project Foundation of Guilin University of Electronic Technology (No. 2016YJCX0).

Author information

Authors and Affiliations

  1. School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guangxi, Guilin, 541004, China

    Jiang-Xia Nan, Hong Bo & Cheng-Lin Wei

Authors
  1. Jiang-Xia Nan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hong Bo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Cheng-Lin Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiang-Xia Nan .

Editor information

Editors and Affiliations

  1. Fuzhou University, Fuzhou, Fujian, China

    Deng-Feng Li

  2. Chinese Academy of Sciences, Beijing, China

    Xiao-Guang Yang

  3. University of Twente, Enschede, The Netherlands

    Marc Uetz

  4. Northwestern Polytechnical University, Xi'an, China

    Gen-Jiu Xu

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer Nature Singapore Pte Ltd.

About this paper

Cite this paper

Nan, JX., Bo, H., Wei, CL. (2017). Cooperative Games with the Intuitionistic Fuzzy Coalitions and Intuitionistic Fuzzy Characteristic Functions. In: Li, DF., Yang, XG., Uetz, M., Xu, GJ. (eds) Game Theory and Applications. China GTA China-Dutch GTA 2016 2016. Communications in Computer and Information Science, vol 758. Springer, Singapore. https://doi.org/10.1007/978-981-10-6753-2_24

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-6753-2_24

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-6752-5

  • Online ISBN: 978-981-10-6753-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation