A Spatial Fuzzy Co-Location Pattern Mining Method Based on Interval Type-2 Fuzzy Sets

The goal of spatial co-location pattern mining is to find subsets of spatial features whose instances are often neighbors in a geographical space. In many practical cases, instances of spatial features contain not only spatial location information but also attribute information. Although there have been several studies that use type-1 fuzzy membership functions to mine spatial fuzzy co-location patterns, there is great uncertainty associated with such membership functions. To address this problem, we propose a spatial fuzzy co-location pattern mining method based on interval type-2 fuzzy sets. First, we collect the interval evaluation values of the interval data of attribute information from experts to form granular data. Next, the original type-1 fuzzy membership function is extended to a granular type-2 fuzzy membership function based on elliptic curves. We use a gradual method to adjust the parameters of the fuzzy membership function so that its footprint of uncertainty satisfies both the connectivity and the given confidence. Based on this granular type-2 fuzzy membership function, we fuzzify the attribute information of instances and define the concepts of fuzzy features and fuzzy co-location patterns. A fuzzy co-location pattern mining algorithm based on spatial cliques is then proposed, termed the FCPM-Clique algorithm. In order to improve the efficiency of the algorithm, we propose two pruning strategies. In addition, we extend two classical spatial pattern mining algorithms, the Join-based algorithm and the Joinless algorithm, to mine fuzzy co-location patterns based on interval type-2 fuzzy sets. Many experiments on synthetic and real-world datasets are conducted, the performance of the three algorithms is compared, and the effectiveness and efficiency of our proposed FCPM-Clique algorithm is demonstrated.