Skip to main content

Study of Mean-Entropy Models for Key Point Air Defense Disposition

  • Conference paper
Fuzzy Information and Engineering 2010

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 78))

  • 1059 Accesses

Abstract

Air defense disposition problem is full of uncertainties and risks in modern war. In this paper, entropy is used as a measure of risk. The smaller entropy value is, the less uncertainty the problem contains, and thus, the safer disposition is. Within the framework of uncertainty theory, two types of fuzzy mean-entropy models are proposed. And a hybrid intelligent algorithm is presented for solving the proposed models in general cases. To illustrate the effectiveness of the proposed algorithm, a Numerical example of the bi-layer air-defense disposition for air defense operation in uncertain environment is presented.

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 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Liu, B.: Uncertainty Theory: An Introduction to its Axiomatic Foundations. Springer, Berlin (2004)

    MATH  Google Scholar 

  2. Liu, B.: A survey of credibility theory. Fuzzy Optimization and Decision Making 5(4), 387–408 (2006)

    Article  MathSciNet  Google Scholar 

  3. Liu, B., Liu, Y.K.: Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans. Fuzzy syst. 10(4), 445–450 (2002)

    Article  Google Scholar 

  4. Che, M., Grellmann, W., Seidler, S.: Appl. Polym. Sci. 64, 1079–1090 (1997)

    Google Scholar 

  5. De Luca, A., Termini, S.: A definition of nonprobabilistic entropy in the setting of fuzzy sets theory. Inf. Control 20, 301–312 (1972)

    Article  MATH  Google Scholar 

  6. Bhandari, D., Pal, N.R.: Some new information measures of fuzzy sets. Inf. Sci. 67, 209–228 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  7. Liu, B.: Theory and Practice of Uncertain Programming. Physica-verlag, Heidelberg (2002)

    MATH  Google Scholar 

  8. Kaufmann, A.: Introduction to the Theory of Fuzzy Subsets, vol. I. Academic, New York (1975)

    MATH  Google Scholar 

  9. Kosko, B.: Fuzzy entropy and conditioning. Inf. Sci. 40, 165–174 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  10. Li, P., Liu, B.: Entropy and credibility distribution for fuzzy variables. IEEE Trans. Fuzzy Syst. 16, 123–129 (2008)

    Article  Google Scholar 

  11. Liu, B.: A survey of entropy of fuzzy variables. J. Uncertain Syst. 1, 4–13 (2007)

    Google Scholar 

  12. Wang, Y., Zeng, S.: Two fuzzy models for multilayer air defense disposition in fuzzy environment. Fuzzy Information and Engineering 2, 1355–1364 (2009)

    Article  Google Scholar 

  13. Shannon, C.E.: The Mathematical Theory of Communication. Univ. of Illinois Press, Urbana (1949)

    MATH  Google Scholar 

  14. Philippatos, G.C., Wilson, C.J.: Entropy, market risk, and the selection of efficient portdolios. Appl. Econ. 4, 209–220 (1975)

    Article  Google Scholar 

  15. Markowitz, H.: Portfolio selection. J. Finance 7, 777–791 (1952)

    Article  Google Scholar 

  16. Liu, B.: Theory and Practice of Uncertain Programming. Physica-verlag, Heidelberg (2002)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wang, Y., Pan, Lp. (2010). Study of Mean-Entropy Models for Key Point Air Defense Disposition. In: Cao, By., Wang, Gj., Guo, Sz., Chen, Sl. (eds) Fuzzy Information and Engineering 2010. Advances in Intelligent and Soft Computing, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14880-4_71

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14880-4_71

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14879-8

  • Online ISBN: 978-3-642-14880-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics