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The representation and application of fuzzy knowledge on the semantic Web often relate to the comparisons between fuzzy membership degrees. However, the current fuzzy extensions of description logics do not support the expression of such comparisons. This paper proposes an extended fuzzy description logic that supports the comparisons of fuzzy membership degrees and the concept constructors from description logic ALCN (attributive concept description language with complements and number restriction), written FCALCN (fuzzy comparable ALCN). FCALCN introduces new forms of atom concepts in order to support the comparisons between fuzzy membership degrees. A reasoning algorithm for FCALCN is proposed, and the complexity of the reasoning problems of FCALCN with empty TBox is proved to be PSpace-complete. FCALCN can represent expressive fuzzy knowledge involving the comparisons of fuzzy membership degrees on the semantic Web and enable reasoning of them.

Extended Fuzzy Description Logics with Comparisons Between Fuzzy Membership Degrees