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Fuzzy-c-Means and Kriging for Mapping Soil as a Continuous System

Dep. of Soil Science, Waite Agricultural Research Institute, Univ. of Adelaide, Glen Osmond, SA 5064, Australia

Alex B. McBratney

School of Crop Sciences, Univ. of Sydney, Sydney, NSW 2006, Australia

*Corresponding author.

ABSTRACT

Even though soil has long been recognized as a continous system in both the geographical and taxonomic context, there has been no practical approach to mapping soil as a continuum. Fuzzy set theory and the regionalized variable theory provide for such an approach. A predetermined optimal sampling scheme was used for sampling of pedons in an area of 627 by 375 m. The fuzzy-c-means (FCM) algorithm was first used to quantify the pedons into intragrade and extragrade classes by minimization of the fuzzy objective function. The resulting matrix of membership coefficients was used to determine membership semivariograms for the c + 1 continuous soil classes. The resulting semivariogram parameters were further used for kriging of the membership coefficients, yielding an isarithmic map for each of the c + 1 fuzzy soil classes. A composite map that presents the core areas of the continuous classification units was produced by overlaying of the isarithmic maps of the c + 1 classes. The significance of this approach to geographical (or soil) information systems is the associated minimum loss of information if fuzzy logic and operations are integrated into the systems.

Contribution from the Dep. of Soil Science, Univ. of Adelaide, and the School of Crop Sciences, Univ. of Sydney.

Received for publication November 12, 1991.

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