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

Jorge Guevara (1) , Roberto Hirata (2) , Stéphane Canu (3)

1 VISION - Computer vision research group
2 USP - Universidade de São Paulo = University of São Paulo
3 LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes

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.

Mots clés: fuzzy set similarity; kernel on fuzzy sets; fuzzy distance. kernel hypothesis testing

Domaines: Apprentissage [cs.LG]

Jorge Guevara, Roberto Hirata, Stéphane Canu. Fuzzy Set Similarity using a Distance-Based Kernel on Fuzzy Sets. 2015. ⟨hal-01235834v2⟩