he current research progresses and the existing problems of smantics representation of the semantic Web are analyzed. A kind of new fuzzy description logic FSHOIQ (fuzzy SHOIQ) for semantics representation of the semantic Web is presented, and the syntax and semantics of FSHOIQ are given. The fuzzy Tableaux of FSHOIQ is presented, then the ABox satisfiability reasoning algorithm of FSHOIQ based on the fuzzy Tableaux is presented, and the correctness of the satisfiability reasoning algorithm is proved. The TBox expansion and elimination methods are presented. It is proved that TBox subsumption reasoning problem may be translated into a satisfiability reasoning problem in FSHOIQ. Theoretical foundation for fuzzy knowledge representation and reasoning of the semantic Web is provided through FSHOIQ.