Possibilistic Network. Social Polarization in the Metropolitan Area of Marseille (France).

This R-script builds and executes a possibilistic network which has the same structure as the Baysesian network proposed by F. Scarella [2] in order to model social polarization in the metropolitan area of Marseille (France). The model can be used to infer a trend scenario of social polarization of the 439 municipalities in the metropolitan area of Marseille (France) in a 10 year time. Within the model, a valorized municipality is defined as a municipality where executives and professionals are overrepresented within its resident population; a devalorized municipality is defined as a municipality where the unemployed are overrepresented within its resident population.

The initial data for the study area were elaborated for 2009 and are in the Data_Marseille_2009.txt file. Other auxiliary files are:

 - DependentVariables.txt containing the dependency structure of the possibilistic network

 - VariableModalities.txt containing the values of each variable of the network

- VariableModalities_PlainEnglish.txt gives plain English names to variables and modalities, but is not used by the R-script.

- ModelStructure.png visualizes the DAG structure of the possibilistic network

The network is build using uncertain logical gates ([3], [4]), which are the possibilistic counterpart of  the noisy logical gates used in Bayesian networks [2].  More thorough presentations of the model and of the model results are available in [5] and in [6].

Model results and comparison with Bayesian network results can be explored through an interactive data-visualization at the following address: https://public.tableau.com/profile/fusco#!/vizhome/RepresentingUncertainFutures/Story1

References

[1] Francisco Díez and Marek Druzdzel. "Canonical Probabilistic Models for Knowledge Engineering", Tech. Rep. CISIAN-06-01, version 0.9, April 28, 2007.

[2] Floriane Scarella, La ségrégation résidentielle dans l'espace-temps métropolitain: analyse spatiale et géo-prospective des dynamiques résidentielles de la métropole azuréenne, PhD dissertation, University of Nice Sophia Antipolis, 2014.

[3] Matteo Caglioni, Didier Dubois, Giovanni Fusco, Diego Moreno, Henri Prade, Floriane Scarella, and Andrea Tettamanzi. "Mise en oeuvre pratique de réseaux possibilistes pour modéliser la spécialisation sociale dans les espaces métropolisés", LFA 2014 - Cargèse 22-24 novembre 2014, Cépaduès, Toulouse, ISBN : 9782364931565,  pp. 267-274.

[4] Didier Dubois, Giovanni Fusco, Henri Prade, and Andrea Tettamanzi, "Uncertain Logical Gates in Possibilistic Networks. An Application to Human Geography". In Ch. Beierle and A. Dekhtyar (Eds.). Scalable Uncertainty Management - 9th International Conference, SUM 2015, Québec City, QC, Canada, September 16-18, 2015. Proceedings (ISBN: 978-3-319-23539-4),  Lecture Notes in Artificial Intelligence, vol. 9310, Springer, pp. 249-263.

[5] Didier Dubois, Giovanni Fusco, Henri Prade, and Andrea Tettamanzi, "Uncertain Logical Gates in Possibilistic Networks: Theory and application to human geography", International Journal of Approximate Reasoning, 2016 (in progress).

[6] Giovanni Fusco, Cristina Cao, Didier Dubois, Henri Prade, Floriane Scarella, and Andrea Tettamanzi, Social polarization in the metropolitan area of Marseille. Modelling uncertain knowledge with probabilistic and possibilistic networks, ECTQG 2015 - XIX European Colloquium on Theoretical and Quantitative Geography, Bari (Italy), September 3^rd-7^th 2015, Proceedings, Plurimondi. An International Forum for Research and Debate on Human Settlements, 8 p., 2015.