Typical description logics are limited to dealing with crisp concepts and crisp roles. However, Web applications based on description logics should allow the treatment of the inherent imprecision. Therefore, it is necessary to add fuzzy features to description logics. A family of extended fuzzy description logics is proposed to enable representation and reasoning for complex fuzzy information. The extended fuzzy description logics introduce the cut sets of fuzzy concepts and fuzzy roles as atomic concepts and atomic roles, and inherit the concept and role constructors from description logics. The definitions of syntax, semantics, reasoning tasks, and reasoning properties are given for the extended fuzzy description logic. The extended fuzzy description logics adopt a special fuzzify-method with more expressive power than the previous fuzzy description logics.