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On Random Sets and Belief Functions

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Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ,volume 219)

Keywords

  • Probability Measure
  • Topological Space
  • Compact Space
  • Multivalued Mapping
  • Belief Function

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References

  1. G. Shafer, “Allocations of Probability: A Theory of Partial Belief,” Ph.D. Thesis, Univ. Microfilms, Ann Arbor, Mich.,1974.

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  2. G. Shafer, “A Mathematical Theory of Evidence,” Princeton Univ. Press, Princeton, N.J., 1976.

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  3. A. Dempster, Upper and lower probabilities induced by multivalued mapping, Ann. Math. Statist. 38 (1967), 325–339.

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  5. D. G. Kendall, “Foundations of a Theory of Random Sets” in Stochastic Geometry, pp. 322–376, Wiley, New York, 1974.

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  7. F. Spitzer, “Random Fields and Interacting Particle Systems,” Math. Assos. Amer., Washington, D.C., 1971.

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  8. T. E. Harris, On a class of set-valued Markov processes, Ann. Probability 4 (1976), 175–194.

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  10. G. Debreu, Integration of correspondences, in“Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability (1967),” Vol. II, Part 1, pp. 351–372.

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  11. Cl. Berge, “Espaces Topologiques, Fonctions Multivoques,” Dunod, Paris, 1959.

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  12. G. C. Rota, Theory of Mobius functions, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 2 (1964), 340–368.

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Nguyen, H.T. (2008). On Random Sets and Belief Functions. In: Yager, R.R., Liu, L. (eds) Classic Works of the Dempster-Shafer Theory of Belief Functions. Studies in Fuzziness and Soft Computing, vol 219. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44792-4_5

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  • DOI: https://doi.org/10.1007/978-3-540-44792-4_5

  • Publisher Name: Springer, Berlin, Heidelberg

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