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Uncertain logical gates in possibilistic networks: theory and application to human geography. (English) Zbl 1404.68160
Summary: Possibilistic networks offer a qualitative approach for modeling epistemic uncertainty. Their practical implementation requires the specification of conditional possibility tables, as in the case of Bayesian networks for probabilities. The elicitation of probability tables by experts is made much easier by means of noisy logical gates that enable multidimensional tables to be constructed from the knowledge of a few parameters. This paper presents the possibilistic counterparts of usual noisy connectives (and, or, \(\max\), \(\min\), \(\ldots\)). Their interest and limitations are illustrated on an example taken from a human geography modeling problem. The difference of behavior between probabilistic and possibilistic connectives is discussed in detail. Results in this paper may be useful to bring possibilistic networks closer to applications.
68T37 Reasoning under uncertainty in the context of artificial intelligence
91D20 Mathematical geography and demography
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[1] Antonucci, A., The imprecise noisy-OR gate, (Proc. 14th Int. Conf. on Information Fusion, FUSION’11, Chicago, Il., July 5-8, 1-7, (2011))
[2] Beliakov, G.; Pradera, A.; Calvo, T., Aggregation functions: A guide for practitioners, studies in fuzziness and soft computing, vol. 221, (2007), Springer
[3] Ben Amor, N.; Benferhat, S.; Mellouli, K., Anytime propagation algorithm for MIN-based possibilistic graphs, Soft Comput., 8, 150-161, (2003)
[4] Benferhat, S.; Dubois, D.; Prade, H., Practical handling of exception-tainted rules and independence information in possibilistic logic, Appl. Intell., 9, 101-127, (1998)
[5] Benferhat, S.; Dubois, D.; Garcia, L.; Prade, H., On the transformation between possibilistic logic bases and possibilistic causal networks, Int. J. Approx. Reason., 29, 2, 135-173, (2002) · Zbl 1015.68204
[6] Benferhat, S.; Khellaf, F.; Mokhtari, A., Product-based causal networks and quantitative possibilistic bases, (Proc. FLAIRS Conference, (2004)), 832-837
[7] Benferhat, S.; Levray, A.; Tabia, K., On the analysis of probability-possibility transformations: changing operations and graphical models, (Destercke, S.; Denoeux, T., Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2015, Lecture Notes in Computer Science, vol. 9161, (2015), Springer), 279-289 · Zbl 06507023
[8] Caglioni, M.; Dubois, D.; Fusco, G.; Moreno, D.; Prade, H.; Scarella, F.; Tettamanzi, A., Mise en œuvre pratique de réseaux possibilistes pour modéliser la spécialisation sociale dans LES espaces métropolisés, (Proc. 23d Rencontres Francophones sur la Logique Floue et ses Applications, LFA’14, Cargèse, Corsica, 22-24 oct. 2014, Cépaduès éditions, LFA’14, (2014)), 267-274
[9] Centi, C., Le laboratoire marseillais: chemins d’intégration Métropolitaine et de segmentation sociale, (1996), L’Harmattan Paris
[10] Díez, F.; Drudzel, M., Canonical probabilistic models for knowledge engineering, (2007), Technical Report CISIAD-06-01
[11] Dubois, D.; Fusco, G.; Prade, H.; Tettamanzi, A., Uncertain logical gates in possibilistic networks. an application to human geography, (Scalable Uncertainty Management - 9th International Conference, Proceedings, SUM 2015, Quebec City, QC, Canada, September 16-18, 2015, Lecture Notes in Computer Science, vol. 9310, (2015), Springer), 249-263
[12] Dubois, D.; Prade, H., Possibility theory. an approach to computerized processing of uncertainty, (1988), Plenum Press
[13] Dubois, D.; Prade, H., An overview of ordinal and numerical approaches to causal diagnostic problem solving, (Gabbay, D. M.; Kruse, R., Abductive Reasoning and Learning, The Handbooks of Defeasible Reasoning and Uncertainty Management Systems, vol. 4, (2000), Kluwer Academic Publishers Boston, Mass), 231-280 · Zbl 0971.68149
[14] Dubois, D.; Prade, H.; Sandri, S., On possibility/probability transformations, (Lowen, R.; Roubens, M., Fuzzy Logic, (1993), Kluwer), 103-112
[15] Dubois, D.; Prade, H.; Smets, P., Representing partial ignorance, IEEE Trans. Syst. Man Cybern., 26, 3, 361-377, (1996)
[16] Ferson, S.; Ginzburg, L. R., Different methods are needed to propagate ignorance and variability, Reliab. Eng. Syst. Saf., 54, 133-144, (1996)
[17] Fusco, G.; Scarella, F., Métropolisation et ségrégation sociospatiale. LES flux des migrations résidentielles en PACA, L’Espace Géogr., 40, 4, 319-336, (2011)
[18] Haddad, M.; Leray, P.; Ben Amor, N., Apprentissage des rśeaux possibilistes à partir de donnés, Rev. Intell. Artif., 29, 2, 229-252, (2015)
[19] Henrion, M., Some practical issues in constructing belief networks, (Kanal, L.; Levitt, T.; Lemmer, J., Uncertainty in Artificial Intelligence 3, (1989), Elsevier), 161-173
[20] Jensen, F., Bayesian networks and decision graphs, (2001), Springer New York · Zbl 0973.62005
[21] Piatti, A.; Antonucci, A.; Zaffalon, M., Building knowledge-based expert systems by credal networks: a tutorial, (Baswell, A. R., Advances in Mathematics Research, Vol. 11, (2010), Nova Science Publishers New York)
[22] Parsons, S., Qualitative methods for reasoning under uncertainty, (2001), The MIT Press Cambridge, Mass · Zbl 0998.68178
[23] Parsons, S.; Bigham, J., Possibility theory and the generalized noisy OR model, (Proc. I6th Int. Conf. Inform. Proces. and Mgmt. of Uncertainty, IPMU’96, Granada, (1996)), 853-858
[24] Pearl, J., Fusion, propagation and structuring in belief networks, Artif. Intell., 29, 3, 241-288, (1986) · Zbl 0624.68081
[25] Pearl, J., Probabilistic reasoning in intelligent systems, (1988), Morgan Kaufmann San Mateo, Cal
[26] Peng, Y.; Reggia, J., Plausibility of diagnosis of hypothesis, (Proc. National Conference on Artificial Intelligence, AAAI-86, (1986), AAAI Press), 140-145
[27] Renooij, S.; van der Gaag, L. C.; Parsons, S., Context-specific sign-propagation in qualitative probabilistic networks, Artif. Intell., 140, 1/2, 207-230, (2002) · Zbl 0999.68215
[28] Scarella, F., La ségrégation résidentielle dans l’espace-temps métropolitain: analyse spatiale et géo-prospective des dynamiques résidentielles de la métropole azuréenne, (2014), Université Nice Sophia Antipolis, PhD Thesis
[29] Spohn, W., The laws of belief: ranking theory and its philosophical applications, (2012), Oxford University Press UK
[30] Zadeh, L. A., Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets Syst., 1, 3-28, (1978) · Zbl 0377.04002
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