On the t-transitivity of kernels

B. Moser. On the t-transitivity of kernels. Fuzzy Sets and Systems, volume 157, number 13, pages 1787-1796, 2006.

Autoren
  • Bernhard A. Moser
TypArtikel
JournalFuzzy Sets and Systems
Nummer13
Band157
ISSN0165-0114
Jahr2006
Seiten1787-1796
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 T_cos which is characterized as being the greatest one for which all kernels are T_cos-equivalences. Finally, a way of constructing kernels by means of fuzzy sets is outlined.