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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Liu, B.: Uncertainty Theory: An Introduction to its Axiomatic Foundations. Springer, Berlin (2004)
Liu, B.: A survey of credibility theory. Fuzzy Optimization and Decision Making 5(4), 387–408 (2006)
Liu, B., Liu, Y.K.: Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans. Fuzzy syst. 10(4), 445–450 (2002)
Che, M., Grellmann, W., Seidler, S.: Appl. Polym. Sci. 64, 1079–1090 (1997)
De Luca, A., Termini, S.: A definition of nonprobabilistic entropy in the setting of fuzzy sets theory. Inf. Control 20, 301–312 (1972)
Bhandari, D., Pal, N.R.: Some new information measures of fuzzy sets. Inf. Sci. 67, 209–228 (1993)
Liu, B.: Theory and Practice of Uncertain Programming. Physica-verlag, Heidelberg (2002)
Kaufmann, A.: Introduction to the Theory of Fuzzy Subsets, vol. I. Academic, New York (1975)
Kosko, B.: Fuzzy entropy and conditioning. Inf. Sci. 40, 165–174 (1986)
Li, P., Liu, B.: Entropy and credibility distribution for fuzzy variables. IEEE Trans. Fuzzy Syst. 16, 123–129 (2008)
Liu, B.: A survey of entropy of fuzzy variables. J. Uncertain Syst. 1, 4–13 (2007)
Wang, Y., Zeng, S.: Two fuzzy models for multilayer air defense disposition in fuzzy environment. Fuzzy Information and Engineering 2, 1355–1364 (2009)
Shannon, C.E.: The Mathematical Theory of Communication. Univ. of Illinois Press, Urbana (1949)
Philippatos, G.C., Wilson, C.J.: Entropy, market risk, and the selection of efficient portdolios. Appl. Econ. 4, 209–220 (1975)
Markowitz, H.: Portfolio selection. J. Finance 7, 777–791 (1952)
Liu, B.: Theory and Practice of Uncertain Programming. Physica-verlag, Heidelberg (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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)