one can observe that many approaches only learn crisp relations, that is relations with only 0 and 1 as possible values, so that standard binary classifiers can be modified. In this context, consider examples as inferring protein-protein interaction networks or metabolic networks in bioinformatics [@Yamanishi2004; @Geurts2007].

However, graded relations are observed in many real-world applications [@Doignon1986], resulting in a need for new algorithms that take graded relational information into account. Furthermore, the properties of graded relations have been investigated intensively in the recent fuzzy logic literature[^1], and these properties are very useful to analyze and improve current algorithms. Using mathematical properties of graded relations, constraints can be imposed for incorporating domain knowledge in the learning process, to improve predictive performance or simply to guarantee that a relation with the right properties is learned. This is definitely the case for properties like transitivity when learning similarity relations and preference relations – see e.g. [@Switalski2000; @DeBaets2005; @DeBaets2006; @Diaz2007], but even very basic properties like symmetry, antisymmetry or reciprocity already provide domain knowledge that can steer the learning process. For example, in social network analysis, the notion “person A being a friend of person B" should be considered as a symmetric relation, while 