Skip to main content

Additivity and Superadditivity in N-Person Cooperative Games with Attanassov Intuitionistic Fuzzy Expectations

  • Conference paper
  • First Online:
Computer Information Systems and Industrial Management (CISIM 2018)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 11127))

  • 1159 Accesses

Abstract

In agent-based models, agents are expected to coordinate mutual actions – to cooperate. The cooperation among agents is usually described by tools of game theory. In general, the cooperation of autonomous agents is based on information of perspective gain from cooperation. If the gain from cooperation is at least as high as the gain which agents can receive without cooperation, then this situation can be described by tools of superadditive cooperative games. The information received by agents in the case of real-world systems is not deterministic, and the use of more sophisticated tools is required. Hence, the main aim of this paper is to discuss additivity and superadditivity issues in the case of cooperative games with expectations given as Atanassov intuitionistic numbers.

This work was supported by a GACR 18-01246S.

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

Access this chapter

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. Shoham, Y., Leyton-Brown, K.: Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. Cambridge University Press, Cambridge (2009)

    MATH  Google Scholar 

  2. Zadeh, L.A.: Fuzzy sets. Inf. Control. 8(3), 338–353 (1965). https://doi.org/10.1016/S0019-9958(65)90241-X

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  4. Dubois, D., Gottwals, S., Hajek, P., Kacprzyk, J., Prade, H.: Terminological difficulties in fuzzy set theory - the case of ‘intuitionistic fuzzy sets. Fuzzy Sets Syst. 156(3), 485–491 (2005). https://doi.org/10.1016/j.fss.2005.06.001

    Article  MathSciNet  MATH  Google Scholar 

  5. Li, D.-F.: Decision and Game Theory in Management with Intuitionistic Fuzzy Sets. SFSC, vol. 308. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-40712-3

    Book  MATH  Google Scholar 

  6. Çoker, D.: An introduction to intuitionistic fuzzy topological spaces. Fuzzy Sets Syst. 88(1), 81–89 (1997). https://doi.org/10.1016/S0165-0114(96)00076-0

    Article  MathSciNet  MATH  Google Scholar 

  7. Atanassov, K. T.: Intuitionistic Fuzzy Sets: Theory and Applications. Studies in Fuzziness and Soft Computing. Physica-Verlag, New York (1999). https://doi.org/10.1007/978-3-7908-1876-83

  8. Xu, Z.S., Xia, M.: Induced generalized intuitionistic fuzzy operators. Knowl. Based Syst. 24(2), 197–209 (2011). https://doi.org/10.1016/j.knosys.2010.04.010

    Article  Google Scholar 

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

    Google Scholar 

  10. Mareš, M.: Weak arithmetics of fuzzy numbers. Fuzzy Sets Syst. 91, 143–153 (1997). https://doi.org/10.1016/S0165-0114(97)00136-X

    Article  MathSciNet  MATH  Google Scholar 

  11. Xu, Z.S., Yager, R.R.: Some geometric aggregation operators based on intuitionistic fuzzy sets. Int. J. Gen. Syst. 35, 417–433 (2006). https://doi.org/10.1080/03081070600574353

    Article  MathSciNet  MATH  Google Scholar 

  12. Owen, G.: Game theory, 3rd edn. Academic Press, San Diego (1995)

    MATH  Google Scholar 

  13. Mielcová, E.: Core of n-Person transferable utility games with intuitionistic fuzzy expectations. In: Jezic, G., Howlett, R.J., Jain, L.C. (eds.) Agent and Multi-Agent Systems: Technologies and Applications. SIST, vol. 38, pp. 167–178. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-19728-9_14

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Elena Mielcová .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Mielcová, E., Perzina, R. (2018). Additivity and Superadditivity in N-Person Cooperative Games with Attanassov Intuitionistic Fuzzy Expectations. In: Saeed, K., Homenda, W. (eds) Computer Information Systems and Industrial Management. CISIM 2018. Lecture Notes in Computer Science(), vol 11127. Springer, Cham. https://doi.org/10.1007/978-3-319-99954-8_32

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-99954-8_32

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99953-1

  • Online ISBN: 978-3-319-99954-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics