A kriging method for fuzzy spatial data

Abstract

This paper extends the ordinary kriging prediction method and proposes a trend removal method for observed spatial data represented as LR-fuzzy numbers. To this end, a covariance concept was developed and discussed in the fuzzy domain. Then, a notion of semi-variogram and its empirical estimator were proposed. The proposed semi-variogram exhibited all of the characteristics of a typical semi-variogram in the fuzzy domain. A non-parametric kernel-based method was proposed to remove the trend across the fuzzy data. Some common goodness-of-fit criteria were employed to examine the performance of the proposed kriging prediction method. The proposed method was then put to test using a simulated set of fuzzy data. In order to demonstrate the applicability of this approach, it was applied to a set of pH data in the fuzzy domain to investigate the quality of groundwater. The results proved the potentials of the proposed method for the fuzzy spatial data encountered in real applications.