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

B. Moser. On the relationship of kernels in machine learning and fuzzy similarity relations. number SCCH-TR-0508, 2005.

Autoren
  • Bernhard Moser
TypTechnischer Bericht
NummerSCCH-TR-0508
Jahr2005
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.