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.Nowadays,most co-location mining algorithms only focus on the spatial location information of features,but ignore their attribute information.Although there have been several studies that use type-1 fuzzy membership functions to mine fuzzy co-location patterns,there is great uncertainty associated with such membership functions.To address this problem,we propose a 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(FOU)satisfies both the connectivity and the given confidence.Based on this granular type-2fuzzy membership function,we fuzzify the attribute information of instances and define the concepts of of the upper participation ratio and lower participation ratio of fuzzy features,the upper participation index and lower participation index of fuzzy pattern,the absolutely prevalent fuzzy co-location pattern,the fuzzy co-location pattern with prevalent tendency degree,and the absolutely non-prevalent fuzzy co-location pattern.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 spatial clique and interval type-2 fuzzy sets.Many experiments on synthetic and real-world data sets are conducted,the performance of the three algorithms is commpared,and the effectiveness and efficiency of our proposed FCPM-clique algorithm are demonstrate.