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

Author(s) Bernhard Moser
Title On the relationship of kernels in machine learning and fuzzy similarity relations
Typ Techreport
Institution SCCH
Year 2005
Address Hagenberg, Austria
Number SCCH-TR-0508
SCCH # 0508
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.