the notion “person A defeats person B in a chess game" will be antisymmetric (or, equivalently, reciprocal). Nevertheless, many examples exist, too, where neither symmetry nor antisymmetry necessarily hold, like the notion “person A trusts person B".

In this paper we present a general kernel-based approach that unifies all the above cases into one general framework where domain knowledge can be easily specified by choosing a proper kernel and model structure, while different learning settings are distinguished by means of the loss function. Let ${Q}({v},{v}')$ be a binary relation on an object space ${\mathcal{V}}$, then the following learning settings will be considered in particular:

Crisp relations: when the restriction is made that $Q: {\mathcal{V}}^2 \rightarrow \{0,1\}$, we arrive at a binary classification task with pairs of objects as input for the classifier.

$[0,1]$-valued relations: here it is allowed that relations can take the form $Q: {\mathcal{V}}^2 \rightarrow [0,1]$, resulting in a regression type of learning setting. The restriction to the interval $[0,1]$ is predominantly made because many mathematical frameworks in fields like fuzzy set theory and decision theory are built upon such relations, using the notion of a fuzzy relation, but in general one can account quite easily for real-graded 