Abstract: On the basis of the study of social relations by using classical similarity relation,we began to consider the fuzziness in the social relations．By using the concept of cut set,we studied many properties of social relations satisfying similarity relation (i.e.,fuzzy tolerance relation),such as the segmentation of social relation circles,the activity degree of individuals in the social relations and the cost when an individual accomplishes various tasks．The corresponding algorithms were also presented．Simulations show the proposed model can describe the social relation network satisfying similarity relation effectively.

Key words: Social set theory,Similarity relation,Social relation circle,Activity degree,Cost