Skip to main content
SpringerLink
Log in

Hybrid Models: Probabilistic and Fuzzy Information

  • Conference paper
Synergies of Soft Computing and Statistics for Intelligent Data Analysis

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 190))

Abstract

Under the interpretation of fuzzy set as coherent conditional probability, we study inferential processes starting from a probability distribution (on a random variable) and a coherent conditional probability on “fuzzy conditional events”. We characterize the coherent extensions and we analyze an example proposed by Zadeh.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bhaskara Rao, K.P.S., Bhaskara Rao, M.: Theory of charges: a study of finitely additive measures. Academic Press, London (1983)

    MATH  Google Scholar 

  2. Coletti, G., Gervasi, O., Tasso, S., Vantaggi, B.: Generalized Bayesian inference in a fuzzy context: From theory to a virtual reality application. Comput. Stat. Data Anal. 56(4), 967–980 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Coletti, G., Scozzafava, R.: Characterization of coherent conditional probabilities as a tool for their assessment and extension. Int. J. Uncertain. Fuzz. 4, 103–127 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  4. Coletti, G., Scozzafava, R.: Probabilistic logic in a coherent setting. Trends in Logic, vol. 15. Kluwer, Dordrecht (2002)

    Book  Google Scholar 

  5. Coletti, G., Scozzafava, R.: Conditional probability, fuzzy sets, and possibility: a unifying view. Fuzzy Set. Syst. 144, 227–249 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Coletti, G., Scozzafava, R.: Conditional probability and fuzzy information. Comput. Stat. Data Anal. 51, 115–132 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Coletti, G., Scozzafava, R., Vantaggi, B.: Integrated Likelihood in a Finitely Additive Setting. In: Sossai, C., Chemello, G. (eds.) ECSQARU 2009. LNCS (LNAI), vol. 5590, pp. 554–565. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  8. de Finetti, B.: Sull’impostazione assiomatica del calcolo delle probabilità. Annali Univ. Trieste 19, 3–55 (1949)

    Google Scholar 

  9. de Finetti, B.: Teoria della probabilitá, Einaudi, Torino (1970)

    Google Scholar 

  10. Dubins, L.E.: Finitely additive conditional probabilities, conglomerability and disintegration. Ann. Probab. 3, 89–99 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  11. Frank, M.J.: On the simultaneous associativity of F(x,y) and x + y − F(x,y). Aequationes Math. 19, 194–226 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  12. Lawry, J.: Appropriateness measures: An uncertainty model for vague concepts. Synthese 161, 255–269 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Nguyen, H.T., Wu, B.: Fundamental of Statistics with Fuzzy Data. STUDFUZZ. Springer (2010)

    Google Scholar 

  14. Viertl, R.: Statistical Methods for Non-precise Data. CRC Press, Boca Raton (1996)

    Google Scholar 

  15. Zadeh, L.A.: Probability measures of fuzzy events. J. Math. Anal. Appl. 23, 421–427 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  16. Zadeh, L.A.: Toward a perception-based theory of probabilistic reasoning with imprecise probabilities. J. Stat. Plan. Infer. 105, 233–264 (2002)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dip. Matematica e Informatica, University of Perugia, Perugia, Italy

    Giulianella Coletti

  2. Dip. S.B.A.I., University “La Sapienza”, Rome, Italy

    Barbara Vantaggi

Authors
  1. Giulianella Coletti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Barbara Vantaggi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Giulianella Coletti .

Editor information

Editors and Affiliations

  1. Faculty of Computer Science, Otto-von-Guericke University of Magdebur, Geb. 29, Raum 008, Universitätsplatz 2, Magdeburg, 39106, Germany

    Rudolf Kruse

  2. , FB Informatik & Informationswissenschaft, University of Konstanz, Konstanz, 78457, Germany

    Michael R. Berthold

  3. of Magdeburg, Faculty of Computer Science, Otto-von-Guericke University, Geb. 29, Universitätsplatz 2 008, Magdeburg, 39106, Germany

    Christian Moewes

  4. , Department of Statistics and OR, University of Oviedo, C/ Calvo Sotelo, s/n, Oviedo, 33007, Spain

    María Ángeles Gil

  5. Systems Research Institute, Polish Academy of Sciences, Newelska 6, Warsaw, 01-447, Poland

    Przemysław Grzegorzewski

  6. Systems Research Institute, Polish Academy of Sciences, Newelska 6, Warsaw, 01-447, Poland

    Olgierd Hryniewicz

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Coletti, G., Vantaggi, B. (2013). Hybrid Models: Probabilistic and Fuzzy Information. In: Kruse, R., Berthold, M., Moewes, C., Gil, M., Grzegorzewski, P., Hryniewicz, O. (eds) Synergies of Soft Computing and Statistics for Intelligent Data Analysis. Advances in Intelligent Systems and Computing, vol 190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33042-1_42

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-33042-1_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33041-4

  • Online ISBN: 978-3-642-33042-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation