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Epistemic Uncertainty Modeling: The-state-of-the-art

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Integrated Uncertainty in Knowledge Modelling and Decision Making (IUKM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9376))

Abstract

This paper is about the state-of-the-art of epistemic uncertainty modeling from subjective probability (Thomas Bayes) to fuzzy measures (Michio Sugeno).

Dedicated to Michio Sugeno

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References

  1. Bayes, T.: An essay towards solving a problem in the doctrine of chance. Philo. Trans. Royal Soc. London 58, 370–418 (1763)

    Article  MATH  Google Scholar 

  2. Fox, C.R., Ulkumen, G.: Distinguishing two dimensions of uncertainty. In: Brun, W., et al. (eds.) Perspectives on Thinking, Judging, and Decision Making, Universitetsforlaget, Oslo, Norway, pp. 21–35 (2011)

    Google Scholar 

  3. La De Finetti, B.: Prevision: ses lois logiques, ses spurces subjectives. Ann. H. Poincaré 7, 1–68 (1937)

    MATH  Google Scholar 

  4. Lindley, D.V.: Scoring rules and the inevitability of probability. International Statist. Review 50, 1–26 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  5. Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press (1976)

    Google Scholar 

  6. Zadeh, L.: Fuzzy sets as a basis for a theory of possibility. J. Fuzzy Sets and Systems 1, 3–28 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  7. Sugeno, M.: Theory of fuzzy integrals and its applications, Ph.D. Thesis, Tokyo Institute of Technology (1974)

    Google Scholar 

  8. Goodman, I.R., Nguyen, H.T., Rogers, G.S.: On the scoring approach to admissibility of uncertainty measures in expert systems. J. Math. Anal. and Appl. 159, 550–594 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kardaun, O.J.W.F., et al.: Reflections on Fourteen Cryptic Issues Concerning The Nature of Statistical Inference. International Statistical Review 17(2), 277–318 (2003)

    MATH  Google Scholar 

  10. Swiler, L.P., Paez, T.L., Mayes, R.L.: Epistemic uncertainty quantification tutorial. In: Proceedings of the IMAC-XXVII (2009)

    Google Scholar 

  11. Kolmogorov, A.N.: On logical foundations of probability theory. In: Probability Theory and Mathematical Statistics (Tbilisi). Lecture Notes in Mathematics, vol. 1021, pp. 1–5. Springer (1983)

    Google Scholar 

  12. Kampé de Feriet, J.: La theorie generalisee de l’information et la mesure subjective de l’information. Lecture Notes in Mathematics, vol. 398, pp. 1–35. Springer (1974)

    Google Scholar 

  13. Gierz, G., et al.: A Compendium of Continuous Lattices. Springer (1980)

    Google Scholar 

  14. Nguyen, H.T., Tran, H.: On a continuous lattice approach to modeling of coarse data in systems analysis. J. Uncertain Systems 1(1), 62–73 (2007)

    Google Scholar 

  15. Nguyen, H.T.: Sur les mesures d’information de type Inf. Lecture Notes in Mathematics, vol. 398, pp. 62–75. Springer (1974)

    Google Scholar 

  16. Nguyen, H.T.: A note on the extension principle for fuzzy sets. J. Math. Anal. and Appli. 64, 369–380 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  17. Zadeh, L.A.: Fuzzy sets. Inf. and Control. 8, 338–353 (1965)

    Article  MATH  Google Scholar 

  18. Nguyen, H.T.: On random sets and belief functions. J. Math. Anal. and Appli. 65, 531–542 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  19. Nguyen, H.T.: An Introduction to Random Sets. Chapman and Hall/CRC Press (2006)

    Google Scholar 

  20. Box, G.E.P., Draper, N.R.: Empirical Model-Building and Response Surfaces, p. 424. J. Wiley (1987)

    Google Scholar 

  21. Martin, R., Liu, C.: Inferential models: A framework for prior-free posterior probabilistic inference. J. Amer. Statist. Assoc. 108, 301–313 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  22. Martin, R.: Random sets and exact confidence regions. Sankhya A 76(2), 288–304 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  23. Hajek, K.: Sampling From A Finite Population. Marcel Dekker (1981)

    Google Scholar 

  24. McCauley, J.L.: Dynamics of Markets: Econophysics and Finance. Cambridge University Press (2010)

    Google Scholar 

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Author information

Authors and Affiliations

  1. New Mexico State University, Las Cruces, USA

    Hung T. Nguyen

  2. Chiang Mai University, Chiang Mai, Thailand

    Hung T. Nguyen

Authors
  1. Hung T. Nguyen
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Correspondence to Hung T. Nguyen .

Editor information

Editors and Affiliations

  1. Science and Technology, Japan Advanced Institute of, Nomi, Japan

    Van-Nam Huynh

  2. Science, Dept of Systems Innovation, Osaka University,Graduate School of, Osaka, Japan

    Masahiro Inuiguchi

  3. Université de Technologie de Compiègne, Compiègne, France

    Thierry Demoeux

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Nguyen, H.T. (2015). Epistemic Uncertainty Modeling: The-state-of-the-art. In: Huynh, VN., Inuiguchi, M., Demoeux, T. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2015. Lecture Notes in Computer Science(), vol 9376. Springer, Cham. https://doi.org/10.1007/978-3-319-25135-6_1

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  • DOI: https://doi.org/10.1007/978-3-319-25135-6_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25134-9

  • Online ISBN: 978-3-319-25135-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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