A Fuzzy Cluster-wise Gravity Regression to deal with asymmetric flows

A fuzzy cluster-wise gravity regression is proposed to deal with asymmetric flows by embedding gravity modeling within a fuzzy clustering framework. The method partitions origins into clusters associated with heterogeneous gravity regimes, allowing regression parameters to vary across groups while accounting for uncertainty in cluster assignment through membership degrees. The proposed approach has been applied to flows of tertiary students from 24 European countries in the year 2023. The results are very promising, showing interesting patterns that highlight distinct behaviors and mixed regimes for some fuzzy units.