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Fuzzy Optimization and Decision Making

Erschienen in:

01.12.2013

Joint cumulative distribution functions for Dempster–Shafer belief structures using copulas

verfasst von: Ronald R. Yager

Erschienen in: Fuzzy Optimization and Decision Making | Ausgabe 4/2013

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Abstract

We first introduce the Dempster–Shafer belief structure and highlight its role in the representation of information about a random variable for which our knowledge of the probabilities is interval-valued. We investigate the formation of the cumulative distribution function (CDF) for these types of variables. It is noted that this is also interval-valued and is expressible in terms of plausibility and belief measures. The class of aggregation operators known as copulas are introduced and a number of their properties are provided. We discuss Sklar’s theorem, which provides for the use of copulas in the formulation of joint CDFs from the marginal CDFs of classic random variables. We then look to extend these ideas to the case of joining the marginal CDFs associated with Dempster–Shafer belief structures. Finally we look at the formulation CDFs obtained from functions of multiple D–S belief structures.

Vorheriger Artikel A VIKOR-based method for hesitant fuzzy multi-criteria decision making

Nächster Artikel On the convergence of some possibilistic clustering algorithms

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Cherubini, U., Luciano, E., & Vecchiato, W. (2004). Copula methods in finance. New York: Wiley.CrossRefMATH

Dempster, A. P. (1967). Upper and lower probabilities induced by a multi-valued mapping. The Annals of Mathematical Statistics, 38, 325–339.MathSciNetCrossRefMATH

Dempster, A. P. (2008). The Dempster–Shafer calculus for statisticians. International Journal of Approximate Reasoning, 48, 365–377.MathSciNetCrossRefMATH

Denoeux, T., & Zouhal, L. M. (2001). Handling possibilistic labels in pattern classification using evidential reasoning. Fuzzy Sets and Systems, 122, 47–62.MathSciNetCrossRef

Durante, F., & Sempi, C. (2010). Copula theory: An introduction. In P. Jaworski, F. Durante, W. Hardle, & T. Rychlik (Eds.), Copula theory and its applications (pp. 3–31). Berlin: Springer.CrossRef

Fu, C., & Yang, S. L. (2011). Analyzing the applicability of Dempster’s rule to the combination of interval-valued belief structures. Expert Systems with Applications, 38, 4291–4301.CrossRef

Jaffray, J. Y. (1994). Dynamic decision making with belief functions. In R. R. Yager, J. Kacprzyk, & M. Fedrizzi (Eds.), Advances in the Dempster–Shafer theory of evidence (pp. 331–352). New York: Wiley.

Janssens, S., De Baets, B., & De Meyer, H. (2004). Bell-type inequalities for quasi-copulas. Fuzzy Sets and Systems, 148, 263–278.MathSciNetCrossRefMATH

Jaworski, P., Durante, F., Hardle, W. K., & Rychlik, T. (2010). Copula theory and its application. Berlin: Springer.CrossRef

Klement, E. P., Mesiar, R., & Pap, E. (2000). Triangular norms. Dordrecht: Kluwer.CrossRefMATH

Liu, L., & Yager, R. R. (2008). Classic works of the Dempster–Shafer theory of belief functions: An introduction. In R. R. Yager & L. Liu (Eds.), Classic works of the Dempster–Shafer theory of belief functions (pp. 1–34). Heidelberg: Springer.CrossRef

Llinas, J., Nagi, R., Hall, D. L., & Lavery, J. (2010). A multi-disciplinary university research initiative in hard and soft information fusion: Overview, research strategies and initial results. In Proceedings of the 13th international conference on information fusion (Fusion 2010). Edinburgh, UK: Unpaginated.

Masson, M. H., & Denoeux, T. (2011). Ensemble clustering in the belief functions framework. International Journal of Approximate Reasoning, 52, 92–109.MathSciNetCrossRefMATH

McNeil, A. J., Frey, R., & Embrechts, P. (2005). Quantitative risk management. Princeton: Princeton University Press.MATH

Moore, R. E. (1966). Interval analysis. Englewood Cliff, NJ: Prentice-Hall.MATH

Nelsen, R. B. (1999). An introduction to copulas. New York: Springer.CrossRefMATH

Papoulis, A. (1965). Probability, random variables and stochastic processes. New York: McGraw-Hill.MATH

Shafer, G. (1976). A mathematical theory of evidence. Princeton, NJ: Princeton University Press.MATH

Sklar, A. (1959). Fonctions dérepartition à n dimensions et leurs marges. Publications of the Institute Statistics University Paris, 8, 229–231.MathSciNet

Sklar, A. (1973). Random variables, joint distributions and copulas. Kybernetica, 9, 449–460.MathSciNetMATH

Smets, P., & Kennes, R. (1994). The transferable belief model. Artificial Intelligence, 66, 191–234.MathSciNetCrossRefMATH

Trivedi, P. K., & Zimmer, D. M. (2007). Copula modeling: An introduction for practitioners. Boston: Now.

Yager, R. R. (2004). Cumulative distribution functions from Dempster–Shafer belief structures. IEEE Transactions on Systems, Man and Cybernetics, Part B, 34, 2080–2087.CrossRef

Yager, R. R. (2006). Modeling holistic fuzzy implication operators using co-copulas. Fuzzy Optimization and Decision Making, 5, 207–226.MathSciNetCrossRefMATH

Yager, R. R., & Liu, L. (2008). Classic works of the Dempster–Shafer theory of belief functions. Heidelberg: Springer.

Yager, R. R., Kacprzyk, J., & Fedrizzi, M. (1994). Advances in the Dempster–Shafer theory of evidence. New York: Wiley.MATH

Yamada, K. (2008). A new combination of evidence based on compromise. Fuzzy Sets and Systems, 159, 1689–1708.MathSciNetCrossRefMATH

Titel: Joint cumulative distribution functions for Dempster–Shafer belief structures using copulas
verfasst von: Ronald R. Yager
Publikationsdatum: 01.12.2013
Verlag: Springer US
Erschienen in: Fuzzy Optimization and Decision Making / Ausgabe 4/2013
Print ISSN: 1568-4539
Elektronische ISSN: 1573-2908
DOI: https://doi.org/10.1007/s10700-013-9163-z

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