AbstractInformation imprecision and uncertainty exist in many real world applications, and such information would be retrieved, processed, shared, reused, and aligned in the maximum automatic way possible. As a popular family of formally well-founded and decidable knowledge representation languages, fuzzy Description Logics (fuzzy DLs), which extend DLs with fuzzy logic, are very well suited to cover for representing and reasoning with imprecision and uncertainty. Thus, a requirement naturally arises in many practical applications of knowledge-based systems, in particular the Semantic Web, because DLs are the logical foundation of the Semantic Web. Currently, there have been lots of fuzzy extensions of DLs with Zadeh's fuzzy logic theory papers published, to investigate fuzzy DLs and more importantly serve as identifying the direction of fuzzy DLs study. In this paper, we aim at providing a comprehensive literature overview of fuzzy DLs, and we focus our attention on fuzzy extensions of DLs based on fuzzy set theory. Other relevant formalisms that are based on approaches like probabilistic theory or non-monotonic logics are covered elsewhere. In detail, we first introduce the existing fuzzy DLs (including the syntax, semantics, knowledge base, and reasoning algorithm) from the origin, development (from weaker to stronger in expressive power), some special techniques, and so on. Then, the other important issues on fuzzy DLs, such as reasoning, querying, applications, and directions for future research, are also discussed in detail. Also, we make a comparison and analysis.
Reasoning with qualified cardinality restrictions in fuzzy Description Logics
