Abstract
Fuzzy measures are used to describe interactions among given attributes towards a certain target. Given an observation as a function defined on the set of attributes, an integral of the function with respect to a given fuzzy measure is usually taken as an aggregation tool in information fusion. Various types of integrals represent different coordination modes of attributes. Thus, in case the coordination mode is unknown, due to the nonadditivity of the fuzzy measure, the integral value is uncertain and varies according to the type of the integral. A commonly used type of fuzzy measures are believe measures. The coordination uncertainty associated with belief measures in information fusion is discussed. Furthermore, the behavior of coordination uncertainty under the Dempster rule of combination is investigated in this paper.
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
Choquet, G.: Theory of capacities. Annales de l’Institut Fourier 5, 131–295 (1954)
Halmos, P.R.: Measure Theory. Van Nostrand, New York (1967)
Shafer, G.: A mathematical theory of Evidence. Princeton University Press, Princeton (1976)
Sugeno, M.: Theory of Fuzzy Integral and its Applications, Ph. D. dissertation, Tokyo Institute of Technology (1974)
Wang, Z., Klir, G.J.: Fuzzy Measure Theory. Plenum, New York (1992)
Wang, Z., Leung, K.S.: Uncertainty carried by fuzzy measures in aggregation. In: Proc. IPMU 2006, pp. 105–112 (2006)
Wang, Z., Leung, K.S., Klir, G.J.: Integration on finite sets. International Journal of Intelligent Systems 21, 1073–1092 (2006)
Wang, Z., et al.: Lower integrals and upper integrals with respect to nonadditive set functions, submitted to FSS
Winston, W.L.: Operations Research— Applications and Algorithms, 4th edn. Duxbury Press, Pacific Grove (2004)
Yager, R.R.: On the Dempster-Shafer framework and new combination rules. Information Sciences 41, 93–137 (1987)
Zadeh, L.A.: A simple view of the Dempster-Shafer theory of evidence and its implication for the rule of combination. AI Magazine 7, 85–90 (1986)
Zong, T., Shi, P., Wang, Z.: The Choquet integral, lower integral, and upper integral on finite sets. In: Proc. IPMU 2006, pp. 2456–2463 (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Wang, Z., Klir, G.J. (2007). Coordination Uncertainty of Belief Measures in Information Fusion. In: Melin, P., Castillo, O., RamÃrez, E.G., Kacprzyk, J., Pedrycz, W. (eds) Analysis and Design of Intelligent Systems using Soft Computing Techniques. Advances in Soft Computing, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72432-2_54
Download citation
DOI: https://doi.org/10.1007/978-3-540-72432-2_54
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72431-5
Online ISBN: 978-3-540-72432-2
eBook Packages: EngineeringEngineering (R0)