Scalarization methods are among the basic approaches for dealing with multi-objective optimization problems. A class of special vector sets is considered, in which both the state variables and state vectors have availability or failure attribute. Firstly, the characteristic function is introduced to carry out scalarization processing on the state vectors in the vector sets, and the critical failure parameter is introduced to approximately characterize the state attributes of the state vectors. Further, under a certain ordering of the state variables of the state vectors according to the failure probability, the reduction properties of the vector sets with state attributes are studied and a reduction algorithm for the vector sets is proposed by means of the scalarization method. Finally, numerical experiments are carried out by taking the RBTS system in the field of power system reliability as an example. The experimental results show that under the appropriate critical failure parameter, the method proposed has a very good reduction effect on the vector sets with state attributes.