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Title of Journal: Soft Comput

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Abbravation: Soft Computing

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Springer-Verlag

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10.1002/ajhb.1310040516

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1433-7479

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A fuzzy interval analysis approach to kriging with

Authors: Kevin Loquin Didier Dubois
Publish Date: 2011/11/10
Volume: 16, Issue: 5, Pages: 769-784
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Abstract

Geostatistics is a branch of statistics dealing with spatial phenomena Kriging consists in estimating or predicting a spatial phenomenon at nonsampled locations from an estimated random function It is assumed that under some wellchosen simplifying hypotheses of stationarity the probabilistic model ie the random function describing spatial variability dependencies can be completely assessed from the dataset However in the usual kriging approach the choice of the random function is mostly made at a glance by the experts ie geostatisticians via the selection of a variogram from a thorough descriptive analysis of the dataset Although information necessary to properly select a unique random function model seems to be partially lacking geostatistics in general and the kriging methodology in particular does not account for the incompleteness of the information that seems to pervade the procedure The paper proposes an approach to handle epistemic uncertainty appearing in the kriging methodology On the one hand the collected data may be tainted with errors that can be modelled by intervals or fuzzy intervals On the other hand the choice of parameter values for the theoretical variogram an essential step contains some degrees of freedom that are seldom acknowledged In this paper we propose to account for epistemic uncertainty pervading the variogram parameters and possibly the dataset and lay bare its impact on the kriging results improving on previous attempts by Bardossy and colleagues in the late 1980sThis work is supported by the French Research National Agency ANR through the textCO 2 program project CRISCO2 ANR06CO2003 The data were kindly provided to us by JeanPaul Chilès and originates from the French institute IRSN Institut de Radioprotection et de Sûreté nucléaire The authors wish to thank JeanPaul Chilès and Nicolas Desassis for their comments on a first draft of this paper and their support during the project

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