Roughness of disturbing fuzzy sets

Firstly,by combining the disturbing fuzzy set theory with the fuzzy set theory,the concept of the rough disturbing fuzzy set is given and some of the fundamental properties of which are studied.And then,by introducing the definitions of the level upper(lower) boundary areas of the distrubing fuzzy set,the shortcomings that the intersection of the upper approximations of two sets is unequal to the upper approximation of the intersection of two sets(the union of the lower approximations of two sets is unequal to the lower approximation of the union of two sets) are overcomed,which commonly exist in the rough set theory.At last,the roughness of the disturbing fuzzy set with respect to parameters is defined and some properties of the new measures are discussed.