FGB-OPRAm: integrating fuzzy granular-ball and OPRAm for spatial query answering in uncertain environments

This paper addresses the critical problem of spatial query answering in uncertain environments, where traditional methods relying on crisp boundaries often fail to capture the inherent imprecision of spatial data. This is particularly relevant in real-world applications dealing with noisy sensor data, imprecise location reports, or vague spatial descriptions. The challenge lies in effectively representing and reasoning with spatial uncertainty to provide accurate and reliable query results. To overcome these limitations, we propose FGB-OPRAm, a novel framework that integrates the fuzzy granular-ball with the OPRAm spatial reasoning calculus. The fuzzy granular-ball, defined using a Gaussian membership function with radius [Formula: see text] representing the level of uncertainty, allow for a flexible representation of spatial regions. OPRAm, a qualitative spatial reasoning calculus, is adapted to operate on these fuzzy granular-balls, enabling reasoning about spatial relationships under uncertainty through fuzzy intersection and containment operations. We evaluate our approach through a series of experiments using OpenStreetMap data, comparing its performance against crisp region baselines, probabilistic KDE models, and deep learning methods like SpaBERT, ST-Transformer, and GNNs. Our results demonstrate that FGB-OPRAm consistently outperforms the crisp baseline, particularly in scenarios with high location noise and angular uncertainty, achieving an F1-score of 0.82 at a 50 m noise level compared to the crisp baseline’s 0.60 ([Formula: see text]). While FGB-OPRAm exhibits higher computational costs, the significant improvements in accuracy, especially in complex combined distance and direction queries (F1-score of 0.85), highlight its potential for applications where accurate spatial reasoning under uncertainty is paramount, offering a directional accuracy of 8 degrees and a Hausdorff distance of 75 m. (The data used in this study is publicly available at https://github.com/bongjaekwon/FGB-OPRAm-SQAUE.)