Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
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)
Coletti, G., Scozzafava, R.: From conditional events to conditional measures: a new axiomatic approach. Annals of Mathematics and Artificial Intelligence 32, 373–392 (2001)
Coletti, G., Scozzafava, R.: Probabilistic Logic in a Coherent Setting. Trends in Logic, vol. 15. Kluwer Academic Publishers, Dordrecht (2002)
Coletti, G., Scozzafava, R.: Toward a general theory of conditional beliefs. Int. J. of Intelligent Systems 21, 229–259 (2006)
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)
Coletti, G., Scozzafava, R., Vantaggi, B.: Inferential processes leading to possibility and necessity. Submitted to Information Sciences
Coletti, G., Vantaggi, B.: T-conditional possibilities: coherence and inference. Fuzzy Sets and Systems 160(3), 306–324 (2009)
de Finetti, B.: Problemi determinati e indeterminati nel calcolo delle probabilitá. Rendiconti della R.Accademia Nazionale dei Lincei 12, 367–373 (1930)
de Cooman, G., Aeyels, D.: Supremum-preserving upper probabilities. Information Sciences 118, 173–212 (1999)
de Cooman, G., Miranda, E., Couso, I.: Lower previsions induced by multi-valued mappings. J. of Statistical Planning and Inference 133, 173–197 (2005)
de Cooman, G., Troffaes, M., Miranda, E.: n-monotone lower previsions. J. of Intelligent and Fuzzy Systems 16(4), 253–263 (2005)
Denneberg, D.: Non-Additive Measure and Integral. Kluwer, Berlin (1997)
Dubois, D., Prade, H.: When upper probabilities are possibility measures. Fuzzy Sets and Systems 49, 65–74 (1992)
Grabisch, M.: k-order additive discrete fuzzy measures and their representation. Fuzzy Sets and Systems 92(2), 167–189 (1997)
Halpern, J.: Reasoning about uncertainty. The MIT Press (2003)
Mesiar, R.: k-order additivity and maxitivity. Atti Sem. Mat. Fis. Univ. Modena 51, 179–189 (2003)
Walley, P.: Statistical reasoning with Imprecise Probabilities. Chapman and Hall, London (1991)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Coletti, G., Scozzafava, R., Vantaggi, B. (2012). Coherence for Uncertainty Measures Given through ⊕-Basic Assignments Ruled by General Operations. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31724-8_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-31724-8_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31723-1
Online ISBN: 978-3-642-31724-8
eBook Packages: Computer ScienceComputer Science (R0)