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A Kernel-Based Multidimensional Fuzzy Water Poverty Index: Evidence from a High-Dimensional Empirical Application
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DOI：10.1016/j.fss.2026.110013.png)
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Abstract
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This paper develops a kernel-based multidimensional fuzzy water poverty index for territorial water-security assessment. The approach first maps household water disadvantages into graded fuzzy memberships and then aggregates them at the regional level through a distributional distance rather than through an additive score. For each territory, the joint distribution of household fuzzy deprivation profiles is compared with the benchmark of full water security by means of the Maximum Mean Discrepancy. The resulting K–FWPI is therefore a regional index, not a household-level deprivation score. It measures distance from water security while preserving information on the clustering and dependence of deprivation dimensions. The framework is demonstrated on a transparent, fully reproducible synthetic dataset of household water-security profiles built from twelve deprivation variables covering affordability, access, continuity, quality, coping costs, seasonal stress, drought exposure and infrastructure fragility. The data-generating process is documented in full, and the entire set of reported quantities is computed from the simulated profiles. The results show that the kernel index separates regions by both the intensity and the clustering of deprivation, and that it distinguishes dispersed from clustered multidimensional deprivation in a controlled exercise where additive fuzzy means are identical by construction. Robustness checks based on alternative bandwidths and a Laplace kernel preserve the regional ordering. The paper contributes to fuzzy poverty measurement by combining membership-based representation with a non-separable kernel aggregation rule defined on distributions of deprivation profiles.
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