This paper defines the concept of derived set operator,introduces the concept of fuzzy derived set operator in EX,studies their properties and discusses their relations to topology.

In order to achieve simply and effectively the ideal edge of a medical image and thus perform an effective medical diagnose, a fast edge detection method based on the combination of fuzzy subsets is developed.

In view of the shortcomings of poor structure features and systematicness of current fuzziness metric,by combining fuzziness characteristic function with fuzziness-synthesizing operator,we establish F+S fuzziness metric model,and give tectonic models of the fuzziness characteristic function based on quasi-linear function and synthesizing operator model based on measure theory.