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Fuzzy Description Logics (Fuzzy DLs) are logics that allow to deal with structured knowledge affected by fuzziness. Fuzzy DLs are at the heart of Fuzzy OWL 2, a fuzzy version of the standard ontology language OWL 2. Although a relatively important amount of work has been carried out in the last years, fuzzy DLs are open to be extended with several features worked out in other fields. In particular, the integration of aggregation operators (AOs) in fuzzy DLs has received little attention so far. In this work, we show how to support aggregation operators in fuzzy DLs. We provide syntax and semantics of a fuzzy DL extended with AOs, and provide a calculus for a family of AOs (weighted sum, OWA and quantifier-guided OWA). We also show how to encode them into our proposal for Fuzzy OWL 2.

We present a novel Fuzzy Description Logic (DL) based approach to automate matchmaking in e-marketplaces. We model traders' preferences with the aid of Fuzzy DLs and, given a request, use utility values computed w.r.t. Pareto agreements to rank a set of offers. In particular, we introduce an expressive Fuzzy DL, extended with concrete domains in order to handle numerical, as well as non numerical features, and to deal with vagueness in buyer/seller preferences. Hence, agents can express preferences as eg textit{I am searching for a passenger car costing about 22000euro, yet if the car has a GPS system and more than two-year warranty I can spend up to 25000euro}. Noteworthy our matchmaking approach, among all the possible matches, chooses the mutually beneficial ones.

Fuzzy Description Logics (fuzzy DLs) have been proposed as a language to describe structured knowledge with vague concepts. In [19], a solution based on Mixed Integer Linear Programming has been proposed to deal with fuzzy DLs under Lukasiewicz semantics in which typical membership functions, such as triangular and trapezoidal functions, can be explicitly represented in the language. A major theoretical and computational limitation so far is the inability to deal with General Concept Inclusions (GCIs), which is an important feature of classical DLs. In this paper, we address this issue and develop a calculus for fuzzy DLs with GCIs under various semantics: classical logic, \Zadeh semantics", and Lukasiewicz logic.

For practical ontology-based applications representing and reasoning with probabilities is an essential task. For Description Logics with subjective probabilities reasoning procedures for testing instance relations based on the completion method have been developed. In this paper we extend this technique to devise algorithms for solving non-standard inferences for EL and its probabilistic extension Prob- EL01c: computing the most specific concept of an individual and finding explanations for instance relations.