Fuzzy sets similarity is an important topic of research due to its several theoretical and practical applications. In this chapter, we present a new kind of similarity measure between fuzzy sets having a geometric interpretation in functional spaces. We will use a well-know concept from kernel methods, the kernel, to define a new class of similarity measures between fuzzy sets. This work aims to show how to engineer kernels on fuzzy sets, using some well-know distances between fuzzy sets. The advantage of our approach is that is possible to have a geometrical interpretation of the similarity measure between fuzzy sets. Similarity measures between fuzzy sets computed via positive definite kernels are interpreted as inner products of two functions in a RKHS. On the other hand, more general kernels like symmetric kernels are interpreted as evaluation of functions by symmetric and bilinear forms in more general functional spaces.
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