Generalizing Type-2 Fuzzy Ontologies and Type-2 Fuzzy Description Logics

In the last years, we are witnessing an increase of real-world applications of fuzzy ontologies. Most fuzzy ontologies are based on type-1 fuzzy logic, and type-2 fuzzy ontologies have not yet received such attention so far. Furthermore, there exists an important gap between type-2 knowledge representation formalisms (type-2 Description Logics) and type-2 fuzzy ontology applications. In this paper, we propose a formal framework for type-2 fuzzy ontologies taking into account the needs of existing applications. Essentially, our approach makes it possible to manage some uncertainty in the fuzzy membership functions used in the fuzzy datatypes and in the degrees of truth of the axioms. We define a type-2 Description Logic, a reasoning algorithm, and give a Fuzzy OWL 2 specification of it.