Fuzzy Set Similarity using a Distance-Based Kernel on Fuzzy Sets.

Similarity measures computed by kernels are well studied and a vast literature is available. In this work, we use distance-based kernels to define a new similarity measure for fuzzy sets. In this sense, a distance-based kernel on fuzzy sets implements a similarity measure for fuzzy sets with a geometric interpretation in functional spaces. When the kernel is positive definite, the similarity measure between fuzzy sets is an inner product of two functions on a Reproducing kernel Hilbert space. This new view of similarity measures for fuzzy sets given by kernels leverages several applications in areas as machine learning, image processing, and fuzzy data analysis. Moreover, it extends the application of kernel methods to the case of fuzzy data. We show an application of our method in a kernel hypothesis testing on fuzzy data. [ABSTRACT FROM AUTHOR]