The fuzzy mathematics have made progresses by leaps and bounds since it was born in Which introduces the traditional mathematics limitation， the narration fuzzy mathematics production;Outlines the fuzzy mathematics's Also introducesthe fuzzy mathematics separately the development and the application from domestic and the In view of how the fuzzy mathematics correctly know its fuzziness， the clarity， randomness and also the differences and relations between approximate and fuzziness have carried on the discussion， the fuzzy mathematics and the classical mathematics relations， the fuzziness objective universality has been further cleared Based on fuzzy mathematics' synthesis judgment model， explained how to carry on the comprehensive appraisal of the library with Key words: Fuzzy mathematics; Fuzziness; Library; Using
