Abstract
Belief graphical models, especially the probabilistic ones, have now a long history and they are successfully used in a wide range of tasks and applications. Thanks to independence relations, they allow a compact representation of complex and uncertain information and they greatly simplify the critical tasks of information elicitation, representation and inference. Many alternative belief graphical models have been proposed to overcome the limits of probability theory and take advantage of the decomposability property. This paper surveys most of the works dealing with belief graphical models based on possibility theory, an alternative uncertainty theory particularly suited for dealing with incomplete and qualitative uncertain knowledge.
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Ajroud, A., Benferhat, S.: An approximate algorithm for min-based possibilistic networks. Int. J. Intell. Syst. 29, 615–633 (2014)
Amor, N.B., Benferhat, S.: Graphoid properties of qualitative possibilistic independence relations. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 13(1), 59–96 (2005)
Amor, N.B., Benferhat, S., Dubois, D., Geffner, H., Prade, H.: Independence in qualitative uncertainty frameworks. In: KR 2000, Principles of Knowledge Representation and Reasoning Proceedings of the Seventh International Conference, Breckenridge, Colorado, USA, 11–15 April 2000, pp. 235–246 (2000)
Amor, N.B., Dubois, D., Gouider, H., Prade, H.: Possibilistic conditional preference networks. In: Destercke, S., Denoeux, T. (eds.) ECSQARU 2015. LNCS, vol. 9161, pp. 36–46. Springer, Heidelberg (2015)
Ayachi, R., Amor, N.B., Benferhat, S.: Inference using compiled min-based possibilistic causal networks in the presence of interventions. Fuzzy Sets Syst. 239, 104–136 (2014)
Ayed, R., Bounhas, I., Elayeb, B., Evrard, F., Bellamine-Bensaoud, N.: A possibilistic approach for the automatic morphological disambiguation of Arabic texts. In: International Conference on Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing, Kyoto, Japan. IEEE Computer Society (2012)
Ben Amor, N., Benferhat, S., Mellouli, K.: Anytime propagation algorithm for min-based possibilistic graphs. Soft Comput. 8, 150–161 (2003)
Benferhat, S., Delobelle, J., Tabia, K.: Three-valued possibilistic networks: semantics & inference. In: 2013 IEEE 25th International Conference on Tools with Artificial Intelligence, Herndon, VA, USA, 4–6 November 2013, pp. 38–45 (2013)
Benferhat, S., Dubois, D., Garcia, L., Prade, H.: On the transformation between possibilistic logic bases and possibilistic causal networks. Int. J. Approximate Reasoning 29(2), 135–173 (2002)
Benferhat, S., Khellaf, F., Zeddigha, I.: Negated min-based possibilistic networks. In: Florida Artificial Intelligence Research Society Conference (2016)
Benferhat, S., Lagrue, S., Tabia, K.: Interval-based possibilistic networks. In: Straccia, U., Calì, A. (eds.) SUM 2014. LNCS, vol. 8720, pp. 37–50. Springer, Heidelberg (2014)
Benferhat, S., Levray, A., Tabia, K.: On the analysis of probability-possibility transformations: changing operations and graphical models. In: Destercke, S., Denoeux, T. (eds.) ECSQARU 2015. LNCS, vol. 9161, pp. 279–289. Springer, Heidelberg (2015)
Benferhat, S., Levray, A., Tabia, K.: Probability-possibility transformations: application to credal networks. In: Beierle, C., Dekhtyar, A. (eds.) SUM 2015. LNCS, vol. 9310, pp. 203–219. Springer, Heidelberg (2015)
Benferhat, S., Smaoui, S.: Hybrid possibilistic networks. Int. J. Approx. Reasoning 44(3), 224–243 (2007)
Benferhat, S., Smaoui, S.: Inferring interventions in product-based possibilistic causal networks. Fuzzy Sets Syst. 169(1), 26–50 (2011)
Benferhat, S., Tabia, K.: Inference in possibilistic network classifiers under uncertain observations. Ann. Math. Artif. Intell. 64(2–3), 269–309 (2012)
Benferhat, S., Tabia, K.: Reasoning with uncertain inputs in possibilistic networks. In: Principles of Knowledge Representation, Reasoning: Proceedings of the Fourteenth International Conference, KR 2014, Vienna, Austria, 20–24 July 2014 (2014)
Borgelt, C., Gebhardt, J., Kruse, R.: Graphical models. In: Proceedings of International School for the Synthesis of Expert Knowledge (ISSEK 98), pp. 51–68. Wiley (2002)
Borgelt, C., Kruse, R.: Graphical Models - Methods for Data Analysis and Mining. Wiley, New York (2002)
Borgelt, C., Kruse, R.: Learning possibilistic graphical models from data. IEEE Trans. Fuzzy Syst. 11(2), 159–172 (2003)
Borgwardt, S., Fazzinga, B., Lukasiewicz, T., Shrivastava, A., Tifrea-Marciuska, O.: Preferential query answering over the semantic web with possibilistic networks. In: Kambhampati, S. (ed.) Proceedings of the 25th International Joint Conference on Artificial Intelligence, IJCAI 2016, New York, NY, USA, 9–15 July 2016. AAAI Press (2016)
Bouchon-Meunier, B., Coletti, G., Marsala, C.: Independence and possibilistic conditioning. Ann. Math. Artif. Intell. 35(1–4), 107–123 (2002)
Boughanem, M., Brini, A., Dubois, D.: Possibilistic networks for information retrieval. Int. J. Approx. Reasoning 50(7), 957–968 (2009)
Bounhas, M., Hamed, M.G., Prade, H., Serrurier, M., Mellouli, K.: Naive possibilistic classifiers for imprecise or uncertain numerical data. Fuzzy Sets Syst. 239, 137–156 (2014)
Cayrol, C., Dubois, D., Touazi, F.: Symbolic possibilistic logic: completeness and inference methods. In: Destercke, S., Denoeux, T. (eds.) ECSQARU 2015. LNCS, vol. 9161, pp. 485–495. Springer, Berlin (2015)
Chavira, M., Darwiche, A.: Compiling bayesian networks with local structure. In: Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI), pp. 1306–1312 (2005)
De Campos, C.P.: New complexity results for map in bayesian networks. In: Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence, IJCAI 2011, vol. 3, pp. 2100–2106. AAAI Press (2011)
Destercke, S., Dubois, D., Chojnacki, E.: Transforming probability intervals into other uncertainty models. In: EUSFLAT 2007 Proceedings, vol. 2, pp. 367–373. Universitas Ostraviensis, Ostrava (2007)
Druzdzel, M.J., Van Der Gaag, L.C.: Elicitation of probabilities for belief networks: combining qualitative and quantitative information. In: Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence, UAI 1995, pp. 141–148. Morgan Kaufmann Publishers Inc., San Francisco (1995)
Dubois, D., Foulloy, L., Mauris, G., Prade, H.: Probability-possibility transformations, triangular fuzzy sets, and probabilistic inequalities. Reliable Comput. 10(4), 273–297 (2004)
Dubois, D., Fusco, G., Prade, H., Tettamanzi, A.: Uncertain logical gates in possibilistic networks. An application to human geography. In: Beierle, C., Dekhtyar, A. (eds.) SUM 2015. LNCS, vol. 9310, pp. 249–263. Springer, Heidelberg (2015)
Dubois, D., Prade, H., Theory, P.: An Approach to Computerized Processing of Uncertainty. Plenum Press, New York (1988)
Dubois, D., Prade, H.: The logical view of conditioning and its application to possibility and evidence theories. Int. J. Approx. Reasoning 4(1), 23–46 (1990)
Dubois, D., Prade, H.: Inference in possibilistic hypergraphs. In: Bouchon-Meunier, B., Zadeh, L.A., Yager, R.R. (eds.) IPMU 1990. LNCS, vol. 521, pp. 250–259. Springer, Heidelberg (1991)
Dubois, D., Prade, H.: Possibilistic logic: a retrospective and prospective view. Fuzzy Sets Syst. 144(1), 3–23 (2004)
Dubois, D., Prade, H.: Practical methods for constructing possibility distributions. Int. J. Intell. Syst. 31(3), 215–239 (2016)
Fonck, P.: Conditional independence in possibility theory. In: Proceedings of the Tenth International Conference on Uncertainty in Artificial Intelligence, UAI 1994, pp. 221–226. Morgan Kaufmann Publishers Inc., San Francisco (1994)
Fonck, P.: A comparative study of possibilistic conditional independence and lack of interaction. Int. J. Approximate Reasoning 16(2), 149–171 (1997)
Garcia, L., Sabbadin, R.: Complexity results and algorithms for possibilistic influence diagrams. Artif. Intell. 172(8), 1018–1044 (2008)
Gasse, M., Aussem, A., Elghazel, H.: A hybrid algorithm for bayesian network structure learning with application to multi-label learning. Expert Syst. Appl. 41(15), 6755–6772 (2014)
Gebhardt, J., Kruse, R.: Learning possibilistic networks from data. In: Proceedings 5th International Workshop on Artificial Intelligence and Statistics, Fort Lauderdale, pp. 233–244 (1996)
Guezguez, W., Amor, N.B., Mellouli, K.: Qualitative possibilistic influence diagrams based on qualitative possibilistic utilities. Eur. J. Oper. Res. 195(1), 223–238 (2009)
Haddad, M., Leray, P., Amor, N.B.: Learning possibilistic networks from data: a survey. In: 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (IFSA-EUSFLAT-15), Gijón, Spain, 30 June 2015 (2015)
Heni, A., Amor, N.B., Benferhat, S., Alimi, A.: Dynamic possibilistic networks: representation and exact inference. In: 2007 IEEE International Conference on Computational Intelligence for Measurement Systems and Applications, pp. 1–8, June 2007
Hisdal, E.: Conditional possibilities independence and non interaction. Fuzzy Sets Syst. 1(4), 283–297 (1978)
Howard, R.A., Matheson, J.E.: Influence diagrams. Principles Appl. Decis. Anal. 2, 720–761 (1984)
Joslyn, C.: Towards an empirical semantics of possibility through maximum uncertainty. In: Fourth World Congress of the International Fuzzy Systems Association: Artificial Intelligence, pp. 86–89 (1991)
Klir, G.J., Geer, J.F.: Information-preserving probability-possibility transformations: recent developments. In: Lowen, R., Roubens, M. (eds.) Fuzzy Logic, pp. 417–428. Kluwer Academic Publishers, Dordrecht (1993)
Lang, J.: Possibilistic logic: complexity and algorithms. In: Kohlas, J., Moral, S. (eds.) Algorithms for Uncertainty and Defeasible Reasoning, vol. 5, pp. 179–220. Kluwer Academic Publishers (2001)
Lauritzen, S.L., Spiegelhalter, D.J.: Local computations with probabilities on graphical structures and their application to expert systems. In: Readings in Uncertain Reasoning, pp. 415–448. Morgan Kaufmann Publishers Inc., San Francisco (1990)
De Campos, L.M., Huete, J.F., Moral, S.: Possibilistic independence. In: Proceedings of EUFIT 1995, vol. 1, pp. 69–73 (1995)
Masson, M.-H., Denoeux, T.: Inferring a possibility distribution from empirical data. Fuzzy Sets Syst. 157(3), 319–340 (2006)
Nilsson, N.J.: Probabilistic logic. Artif. Intell. 28(1), 71–88 (1986)
Pearl, J.: Reverend bayes on inference engines: a distributed hierarchical approach. In: Proceedings of the American Association of Artificial Intelligence National Conference on AI, Pittsburgh, PA, pp. 133–136 (1982)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers Inc., San Francisco (1988)
Sangesa, R., Cabs, J., Corts, U.: Possibilistic conditional independence: a similarity-based measure and its application to causal network learning. Int. J. Approximate Reasoning 18(1), 145–167 (1998)
Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)
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)
Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 100, 9–34 (1999)
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Tabia, K. (2016). Possibilistic Graphical Models for Uncertainty Modeling. In: Schockaert, S., Senellart, P. (eds) Scalable Uncertainty Management. SUM 2016. Lecture Notes in Computer Science(), vol 9858. Springer, Cham. https://doi.org/10.1007/978-3-319-45856-4_3
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