Aggregation operators for fuzzy ontologies

Fuzzy ontologies extend classical ontologies to allow the representation of imprecise and vague knowledge. Although a relatively important amount of work has been carried out in the field during the last years and they have been successfully used in several applications, several notions from fuzzy logic have not been considered yet in fuzzy ontologies. Among them are aggregation operators, mathematical functions used to fuse different pieces of information, which is a very common need. Some examples of aggregation operators are weighted sums, Ordered Weighting Averaging operators and fuzzy integrals. In this work, we integrate fuzzy ontologies and aggregation operators. As a theoretical formalism, we provide the syntax and semantics of a fuzzy Description Logic with fuzzy aggregation operators. We provide a reasoning algorithm for the family of operators that are representable using a Mixed Integer Linear Programming optimization problem. We also show how to encode some examples of aggregation operators using the language Fuzzy OWL 2.