A fuzzy rough sets-based data-driven approach for quantifying local and overall fuzzy relations between variables for spatial data

Exploring the relationships between variables is a crucial component in comprehending geographical phenomena. Most existing methods ignore the vagueness hidden in spatial data when quantifying this relation, which may lead to a partial or even wrong understanding of geographical phenomena as vagueness is an intrinsic property of them. This paper uses fuzzy rough sets for quantifying local and overall variable relationships to address this limitation, relying on the consistent degree between variables. This approach uses a sliding window to scan the entire study area and build a local region for each object. The local variable relation is quantified using the local average membership degree to the positive region for each object during the scan. The overall variable relation in the whole study area is quantified using the median value of the local consistent degree between variables in every local region, and the entropy of the normalized local consistent degree is used to measure the corresponding spatial heterogeneity. The proposed method can detect and compare local and overall variable relations. Comparison experiments on five publicly accessible datasets demonstrate the effectiveness of the proposed method and show that it can reveal patterns missed by geographically weighted regression and geographical detectors, as it models rather than ignores vagueness uncertainty.