On the relationship of kernels in machine learning and fuzzy similarity relations

Autoren Bernhard Moser
Titel On the relationship of kernels in machine learning and fuzzy similarity relations
Typ Technischer Bericht
Nummer SCCH-TR-0508
Ort Hagenberg, Austria
Institution SCCH
Abteilung KVS
Jahr 2005
SCCH ID# 508
Abstract

In this paper, we present a view of kernels from a fuzzy set theoretical perspective. Indeed, it turns out that kernels which are positive definite functions have to fulfill a consistency property given by the so-called T-transitivity of a fuzzy T-equivalence relation with respect to the triangular norm T. As a result, we introduce a triangular norm TCos which is characterized as being the greatest one for which all kernels are TCos-equivalences. Finally, a way of constructing kernels by means of fuzzy sets is outlined.