Generation of Plateau-Approximated Fuzzy Zones

Hazaël Jones (1, 2) , Serge Guillaume (2) , Patrice Loisel (1) , Brigitte Charnomordic (1) , Bruno Tisseyre (2)

1 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
2 UMR ITAP - Information – Technologies – Analyse Environnementale – Procédés Agricoles

When modelling spatial real data in environmental context, the border between two zones israrely a sharp edge. Often, the transition from one zone to another is a gradual process. Fuzzy zones intend to model this uncertainty in zones by allowing a spatial point to belong partiallyto different zones with different membership degrees. Generating fuzzy zones is not easy to perform and can be time-consuming and difficult to interpret. It is also difficult to ensure the convexity of the generated fuzzy zones. Our idea is to generate plateau zones instead of fuzzy zones. Plateau zones are an approximation of fuzzy zones. The interest of using plateau zones lies in the following: easier spatial coherence and convexity of zones, preservation of uncertainties, level and number of plateau scan be chosen depending on the application, interpretation and easier operations between zones.Our algorithm is based on quantiles of spatial data in order to produce some iso contours. According to the desired number of plateaus, it is possible to adjust the quantile values to find next plateaus for each resulting zones. The goal of this representation is to provide the user a simplification of the spatial representation and to preserve uncertainties in order to use them in the decision process.

Mots clés: fuzzy sets; mathematical model; spatial representation; multi-objective particle swarm optimization (mopso); applied mathematics

Mots clés: logique floue; modèle mathématique; représentation spatiale; algorithme; mathématiques appliquées

Domaines: Statistiques [math.ST]

Hazaël Jones, Serge Guillaume, Patrice Loisel, Brigitte Charnomordic, Bruno Tisseyre. Generation of Plateau-Approximated Fuzzy Zones. Proceedings of Spatial Accuracy 2016, Jul 2016, Montpellier, France. ⟨hal-01602985⟩