Coherence for Uncertainty Measures Given through ⊕-Basic Assignments Ruled by General Operations

  • Giulianella Coletti
  • Romano Scozzafava
  • Barbara Vantaggi
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 300)


In order to deal with partial assessments and their extensions, we give a characterization of some measures (such as capacities, belief functions, possibilities) in terms of basic assignments ruled by a general operation ⊕. The notion of coherence introduced by de Finetti in the probabilistic setting is generalized to non additive measures and we study the upper and lower envelopes of all possible extensions.


Decomposable measures basic assignment coherence lower and upper envelopes 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baioletti, M., Coletti, G., Petturiti, D., Vantaggi, B.: Inferential models and relevant algorithms in a possibilistic framework. Inter. J. of Approximate Reasoning 52(5), 580–598 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Chateauneuf, A., Jaffray, J.Y.: Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion. Mathematical Social Sciences 17(3), 263–283 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Coletti, G., Scozzafava, R.: From conditional events to conditional measures: a new axiomatic approach. Annals of Mathematics and Artificial Intelligence 32, 373–392 (2001)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Coletti, G., Scozzafava, R.: Probabilistic Logic in a Coherent Setting. Trends in Logic, vol. 15. Kluwer Academic Publishers, Dordrecht (2002)CrossRefGoogle Scholar
  5. 5.
    Coletti, G., Scozzafava, R.: Toward a general theory of conditional beliefs. Int. J. of Intelligent Systems 21, 229–259 (2006)zbMATHCrossRefGoogle Scholar
  6. 6.
    Coletti, G., Scozzafava, R., Vantaggi, B.: Possibility measures through a probabilistic inferential process. In: Proc. Int. Conf. of NAFIPS. IEEE CN: CFP08750-CDR Omnipress, New York (2008)Google Scholar
  7. 7.
    Coletti, G., Scozzafava, R., Vantaggi, B.: Inferential processes leading to possibility and necessity. Submitted to Information SciencesGoogle Scholar
  8. 8.
    Coletti, G., Vantaggi, B.: T-conditional possibilities: coherence and inference. Fuzzy Sets and Systems 160(3), 306–324 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    de Finetti, B.: Problemi determinati e indeterminati nel calcolo delle probabilitá. Rendiconti della R.Accademia Nazionale dei Lincei 12, 367–373 (1930)zbMATHGoogle Scholar
  10. 10.
    de Cooman, G., Aeyels, D.: Supremum-preserving upper probabilities. Information Sciences 118, 173–212 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    de Cooman, G., Miranda, E., Couso, I.: Lower previsions induced by multi-valued mappings. J. of Statistical Planning and Inference 133, 173–197 (2005)zbMATHCrossRefGoogle Scholar
  12. 12.
    de Cooman, G., Troffaes, M., Miranda, E.: n-monotone lower previsions. J. of Intelligent and Fuzzy Systems 16(4), 253–263 (2005)Google Scholar
  13. 13.
    Denneberg, D.: Non-Additive Measure and Integral. Kluwer, Berlin (1997)Google Scholar
  14. 14.
    Dubois, D., Prade, H.: When upper probabilities are possibility measures. Fuzzy Sets and Systems 49, 65–74 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Grabisch, M.: k-order additive discrete fuzzy measures and their representation. Fuzzy Sets and Systems 92(2), 167–189 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Halpern, J.: Reasoning about uncertainty. The MIT Press (2003)Google Scholar
  17. 17.
    Mesiar, R.: k-order additivity and maxitivity. Atti Sem. Mat. Fis. Univ. Modena 51, 179–189 (2003)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Walley, P.: Statistical reasoning with Imprecise Probabilities. Chapman and Hall, London (1991)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Giulianella Coletti
    • 1
  • Romano Scozzafava
    • 2
  • Barbara Vantaggi
    • 2
  1. 1.Università di PerugiaPerugiaItaly
  2. 2.Università La Sapienza di RomaRomaItaly

Personalised recommendations