zbMATH — the first resource for mathematics

On the analysis of probability-possibility transformations: changing operations and graphical models. (English) Zbl 06507023
Destercke, Sébastien (ed.) et al., Symbolic and quantitative approaches to reasoning with uncertainty. 13th European conference, ECSQARU 2015, Compiègne, France, July 15–17, 2015. Proceedings. Cham: Springer (ISBN 978-3-319-20806-0/pbk; 978-3-319-20807-7/ebook). Lecture Notes in Computer Science 9161. Lecture Notes in Artificial Intelligence, 279-289 (2015).
Summary: Representing and reasoning with uncertain information is a common topic in Artificial Intelligence. In this paper, we focus on probability-possibility transformations in the context of changing operations and graphical models. Existing works mainly propose probability-possibility transformations satisfying some desirable properties. Regarding the analysis of the behavior of these transformations with respect to changing operations (such as conditioning and marginalization), only few works addressed such issues. This paper concerns the commutativity of transformations with respect to some reasoning tasks such as marginalization and conditioning. Another crucial issue addressed in this paper is the one of probability-possibility transformations in the context of graphical models, especially the independence of events and variables.
For the entire collection see [Zbl 1316.68008].

68T37 Reasoning under uncertainty in the context of artificial intelligence
Full Text: DOI
[1] Baudrit, C., Couso, I., Dubois, D.: Joint propagation of probability and possibility in risk analysis: towards a formal framework. Int. J. Approximate Reasoning 45(1), 82–105 (2007) · Zbl 1123.68123 · doi:10.1016/j.ijar.2006.07.001
[2] Benferhat, S., Dubois, D., Prade, H.: Possibilistic and standard probabilistic semantics of conditional knowledge bases. J. Log. Comput. 9(6), 873–895 (1999) · Zbl 0945.68166 · doi:10.1093/logcom/9.6.873
[3] Borgelt, C., Kruse, R.: Learning possibilistic graphical models from data. IEEE. Trans. Fuzzy Syst. 11(2), 159–172 (2003) · Zbl 1082.68600 · doi:10.1109/TFUZZ.2003.809887
[4] Darwiche, A.: Modeling and Reasoning with Bayesian Networks. Cambridge University Press, Cambridge (2009) · Zbl 1231.68003 · doi:10.1017/CBO9780511811357
[5] Destercke, S., Dubois, D., Chojnacki, E.: Transforming probability intervals into other uncertainty models. In: 5th EUSFLAT Conference, 11–14 September 2007, Ostrava, Czech Republic. Regular Sessions, vol. 2, pp. 367–373 (2007)
[6] Dubois, D., Fargier, H., Prade, H.: Ordinal and probabilistic representations of acceptance. J. Artif. Int. Res. 22(1), 23–56 (2004) · Zbl 1080.68681
[7] Dubois, D., Foulloy, L., Mauris, G., Prade, H.: Probability-possibility transformations, triangular fuzzy sets, and probabilistic inequalities. Reliable Comput. 10(4), 273–297 (2004) · Zbl 1043.60003 · doi:10.1023/B:REOM.0000032115.22510.b5
[8] Dubois, D., Prade, H.: Possibility Theory: An Approach to Computerized Processing of Uncertainty. Plenum Press, New York (1988) · Zbl 0703.68004 · doi:10.1007/978-1-4684-5287-7
[9] Dubois, D., Prade, H.: Random sets and fuzzy interval analysis. Fuzzy Sets Syst. 42(1), 87–101 (1991). DP165 · Zbl 0734.65041 · doi:10.1016/0165-0114(91)90091-4
[10] Dubois, D., Prade, H., Sandri, S.: On possibility/probability transformations. In: Fuzzy Logic, pp. 103–112 (1993)
[11] Hisdal, E.: Conditional possibilities independence and non interaction. Fuzzy Sets Syst. 1(4), 283–297 (1978) · Zbl 0393.94050 · doi:10.1016/0165-0114(78)90019-2
[12] Klir, G.J., Geer, J.F.: Information-preserving probability- possibility transformations: Recent developments. In: Fuzzy Logic, pp. 417–428 (1993)
[13] Masson, M.-H., Denoeux, T.: Inferring a possibility distribution from empirical data. Fuzzy Sets Syst. 157(3), 319–340 (2006) · Zbl 1083.68125 · doi:10.1016/j.fss.2005.07.007
[14] Billaudel, P., Mouchaweh, M.S., Bouguelid, M.S., Riera, B.: Variable probability-possibility transformation, 417–428, September 2006
[15] Prade, H., Dubois, D.: Random Sets and Fuzzy Interval Analysis. Fuzzy Sets Syst. 42(1), 87–101. Elsevier North-Holland, Inc., Amsterdam (1991) · Zbl 0734.65041
[16] Slimen, Y.B., Ayachi, R., Amor, N.B.: Probability-Possibility Transformation: Application to Bayesian and Possibilistic Networks. In: Masulli, F. (ed.) WILF 2013. LNCS, vol. 8256, pp. 122–130. Springer, Heidelberg (2013) · Zbl 1423.68499 · doi:10.1007/978-3-319-03200-9_13
[17] Snow, P.: Standard probability distributions described by rational default entailment (1996)
[18] Sudkamp, T.: On probability-possibility transformations. Fuzzy Sets Syst. 51, 73–81 (1992) · Zbl 0782.60011 · doi:10.1016/0165-0114(92)90077-H
[19] Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 100, 9–34 (1999) · doi:10.1016/S0165-0114(99)80004-9
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.