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Imprecise (fuzzy) information in geostatistics

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Abstract

A methodology based on fuzzy set theory for the utilization of imprecise data in geostatistics is presented. A common problem preventing a broader use of geostatistics has been the insufficient amount of accurate measurement data. In certain cases, additional but uncertain (soft) information is available and can be encoded as subjective probabilities, and then the soft kriging method can be applied (Journel, 1986). In other cases, a fuzzy encoding of soft information may be more realistic and simplify the numerical calculations. Imprecise (fuzzy) spatial information on the possible variogram is integrated into a single variogram which is used in a fuzzy kriging procedure. The overall uncertainty of prediction is represented by the estimation variance and the calculated membership function for each kriged point. The methodology is applied to the permeability prediction of a soil liner for hazardous waste containment. The available number of hard measurement data (20) was not enough for a classical geostatistical analysis. An additional 20 soft data made it possible to prepare kriged contour maps using the fuzzy geostatistical procedure.

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Authors and Affiliations

  1. Department of Civil Engineering, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    A. Bardossy

  2. Department of Civil Engineering, University of Nebraska-Lincoln, W348 Nebraska Hall, 68588, Lincoln, Nebraska

    I. Bogardi & W. E. Kelly

Authors
  1. A. Bardossy
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  2. I. Bogardi
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  3. W. E. Kelly
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Bardossy, A., Bogardi, I. & Kelly, W.E. Imprecise (fuzzy) information in geostatistics. Math Geol 20, 287–311 (1988). https://doi.org/10.1007/BF00892981

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  • DOI: https://doi.org/10.1007/BF00892981

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