Skip to main content

Matrix Games with Payoffs of Intuitionistic Fuzzy Sets and Linear and Nonlinear Programming Methods

  • Chapter
  • First Online:
Decision and Game Theory in Management With Intuitionistic Fuzzy Sets

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 308))

Abstract

In real-life management situations, there is an important kind of competitive decision problems with multiple decision makers (i.e., players). At present, game theory is one of the most effective tools to deal with such a kind of management problems. In the classical (or crisp) game theory, we usually assume that payoffs of players are crisp (or numerical) values.

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

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and 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

Notes

  1. 1.

    As stated in Foreword, the terms “decision maker” and “player” may be interchangeably used. However, the term “player” is customarily used in game theory.

References

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

    MATH  Google Scholar 

  2. Li, D.-F.: Linear programming approach to solve interval-valued matrix games. Omega: Int. J. Manag. Sci. 39(6), 655–666 (2011)

    Article  Google Scholar 

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

    Google Scholar 

  4. Li, D.-F.: Notes on linear programming technique to solve two person matrix games with interval pay-offs. Asia Pac. J. Oper. Res. 28(6), 705–737 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Li, D.-F., Nan, J.X., Zhang, M.J.: Interval programming models for matrix games with interval payoffs. Optim. Methods Softw. 27(1), 1–16 (2012)

    Article  MathSciNet  Google Scholar 

  6. Li, D.-F.: A fuzzy multiobjective programming approach to solve fuzzy matrix games. Int. J. Fuzzy Math. 7(4), 907–912 (1999)

    MATH  Google Scholar 

  7. 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 

  8. Bector, C.R., Chandra, S.: Fuzzy Mathematical Programming and Fuzzy Matrix Games. Springer-Verlag, Berlin (2005)

    MATH  Google Scholar 

  9. Chankong, V., Haimes, Y.Y.: Multiobjective Decision Making: Theory and Methodology. North-Holland, New York (1983)

    MATH  Google Scholar 

  10. Li, D.-F.: Fuzzy Multiobjective Many Person Decision Makings and Games. National Defense Industry Press, Beijing (2003) (in Chinese)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Deng-Feng Li .

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Li, DF. (2014). Matrix Games with Payoffs of Intuitionistic Fuzzy Sets and Linear and Nonlinear Programming Methods. In: Decision and Game Theory in Management With Intuitionistic Fuzzy Sets. Studies in Fuzziness and Soft Computing, vol 308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40712-3_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-40712-3_7

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40711-6

  • Online ISBN: 978-3-642-40712-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics