Extended fuzzy description logics are fuzzy extensions of description logics, which support representation and reasoning for expressive fuzzy knowledge. But they lack reasoning algorithms with the terminology axioms. This paper defines restricted TBoxes (terminological boxes) to describe terminology axioms in EFALC_R+(extended fuzzy attributive concept description language with complements and transitive roles), proposes and optimizes reasoning algorithms for EFALC_R+ with respect to restricted TBoxes. The optimized reasoning algorithm is proved sound, complete and with a worst complexity of exponential time. Its complexity has reached the lower bound, since the reasoning problem for EFALC_R+ with respect to restricted TBoxes is proved exponential time complete. So it is an efficient algorithm of reasoning for fuzzy knowledge bases with terminology axioms.