| One of the most important issues of Computer Science is the representation of human knowledge and its use for reasoning. Description Logics are a very popular family of knowledge representation languages which were created for this purpose. However, despite their rich expressive power, they are insufficient for application domains that deal with imperfect or fuzzy information. Such kinds of information are contained in concepts such as tall, long, etc that are an integral part of our lives and, therefore, the need for its effective representation is crucial. For this reason fuzzy extensions of Description Logics have been proposed in the literature. Among them, the work of Stoilos et al. that presents a reasoning algorithm for the expressive fuzzy Description Logic f-SHIN is the most important. This work has set the basis for practical reasoning using fuzzy Description Logics but it was not enough. The theoretical complexity of the proposed tableau reasoning algorithm is (2-NEXPTIME), that is very expensive. Therefore an implementation directly based on this very expensive algorithm, would result to a reasoner that could not be applied to real case scenarios. In this thesis we aim at transforming the theoretical formalism of fuzzy Description Logic f-SHIN to a practicable reasoning algorithm. In order to achieve this goal we studied the techniques and the tools that make expressive crisp Description Logics practicable for the representation of various domains. In this research the following results have been achieved. We transformed some optimizations techniques that have been successfully applied to crisp Description Logics in a way that can also be applied to fuzzy Description Logic f-SHIN. We suggested some innovative optimization techniques only for fuzzy Description Logics. Additionally, we implemented the fuzzy reasoning engine FiRE which is the first system implemented for reasoning with expressive fuzzy Descriptive Logics. FiRE has been extended using triple stores to save a fuzzy knowledge base and to support fuzzy conjuctive queries. Furthermore, we assessed the performance of the reasoning system FiRE regarding its reasoning services and its support on fuzzy conjunctive queries. Finally, using the implemented reasoning systems, we have proposed innovative approaches for both the semantic annotation of multimedia content and neura-symbolic integration, based on expressive fuzzy Description Logics.
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