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The Weighted Fuzzy Barycenter: Definition and Application to Forest Fire Control in the PACA Region

The Weighted Fuzzy Barycenter: Definition and Application to Forest Fire Control in the PACA Region
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Author(s): Julio Rojas-Mora (UMR Espace CNRS, Université d’Avignon et des Pays de Vaucluse, Avignon, France & Institute of Statistics, Universidad Austral de Chile, Valdivia, Chile), Didier Josselin (UMR Espace CNRS, Université d’Avignon et des Pays de Vaucluse, Avignon, France), Jagannath Aryal (School of Land and Food, University of Tasmania, Hobart, TAS, Australia), Adrien Mangiavillano (CEREN, Gardanne, France) and Philippe Ellerkamp (UMR Espace CNRS, Université d’Avignon et des Pays de Vaucluse, Avignon, France)
Copyright: 2013
Volume: 4
Issue: 4
Pages: 20
Source title: International Journal of Agricultural and Environmental Information Systems (IJAEIS)
Editor(s)-in-Chief: Petraq Papajorgji (Canadian Institute of Technology, Tirana, Albania) and François Pinet (Irstea/Cemagref - Clermont Ferrand, France)
DOI: 10.4018/ijaeis.2013100103

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Abstract

In this paper, the authors present a methodology to solve the weighted barycenter problem when the data is inherently fuzzy. This method, from data clustered by expert visual inspection of maps, calculates bi-dimensional fuzzy numbers from the spatial clusters, which in turn are used to obtain the weighted fuzzy barycenter of a particular area. The authors apply the methodology, to a particularly apt data set of forest fire breakouts in the PACA region of southeastern France, gathered from 1986 to 2008, and sliced into five periods over which the fuzzy weighted barycenter for each one is obtained. Two weighting schemes based on fire intensity and fire density in a cluster were used. The center provided with this fuzzy method provides leeway to planners, which can see how the membership function of the fuzzy solution can be used as a measurement of “appropriateness” of the final location.

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