An Investigation of Takagi-Sugeno Fuzzy Modeling for Spatial Prediction with Sparsely Distributed Geospatial Data

Abstract

Fuzzy set theory has shown potential for reducing uncertainty as a result of data sparsity and also provides advantages for quantifying gradational changes like those of pollutant concentrations through fuzzy clustering based approaches. The ability to lower the sampling frequency and perform laboratory analyses on fewer samples, yet still produce an adequate pollutant distribution map, would reduce the initial cost of new remediation projects. To assess the ability of fuzzy modeling to make spatial predictions using fewer sample points, its predictive ability was compared with the ordinary kriging (OK) and inverse distance weighting (IDW) methods under increasingly sparse data conditions. This research used a Takagi–Sugeno (TS) fuzzy modelling approach with fuzzy c-means (FCM) clustering to make spatial predictions of the lead concentrations in soil. The performance of the TS model was very dependent on the number of outliers in the respective validation set. For modeling under sparse data conditions, the TS fuzzy modeling approach using FCM clustering and constant width Gaussian shaped membership functions did not show any advantages over IDW and OK for the type of data tested. Therefore, it was not possible to speculate on a possible reduction in sampling frequency for delineating the extent of contamination for new remediation projects.