Rough set describes an uncertain target set with upper and lower approximation sets

and approximation set of rough set uses 0.5-approximation set as an approximation set of the uncertain target set.In this paper

we firstly find that the theory of attribute reduction algorithm based on similarity between target set and its 0.5-approximation set is still incomplete

and this similarity is not sensitive to changing granularities.In order to overcome above shortcomings

the change rule of similarity with changing granularities in a multi-granularity space is analyzed

fuzzy degree of approximation set is defined

and the change rules of this fuzziness with changing granularities are analyzed in detail in a hierarchical space.Finally

a new attribute reduction algorithm is proposed.From a new perspective

a kind of differentiation measure between an uncertain target set and its approximation set is presented.