On the T-transitivity of kernels

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 mapping to the unit interval and having constant 1 in its diagonal are Tcos-equivalences. Finally, some applied relevant aspects are discussed as a starting point for further research. © 2006 Elsevier B.V. All rights reserved.