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.

中文翻译：

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一种模糊空间数据的克里金方法

本文扩展了普通克里金预测方法，并提出了一种以LR-模糊数表示的观测空间数据的趋势去除方法。为此，在模糊域中开发并讨论了协方差概念。然后，提出了半变异函数的概念及其经验估计量。所提出的半变异函数展示了模糊域中典型半变异函数的所有特征。提出了一种基于非参数核的方法来消除模糊数据的趋势。一些常见的拟合优度标准被用来检查所提出的克里金法预测方法的性能。然后使用一组模拟的模糊数据对所提出的方法进行测试。为了证明这种方法的适用性，它被应用于模糊域中的一组 pH 数据，以调查地下水的质量。结果证明了所提出的方法在实际应用中遇到的模糊空间数据的潜力。