Hybrid multi-attribute decision making based on vague sets

In view of the practical problems in hybrid multi-attribute decision-making, a method based on vague sets is proposed. Firstly, the qualitative and quantitative indicator values described by linguistic variables and exact numbers respectively are transformed into vague values. Secondly, a model of hybrid multi-objective decision making based on vague sets is put forward. Thirdly a novel comprehensive evaluation index is proposed, by which the meaning of “which is closest to PIS (Positive Ideal Solution) and farthest from NIS (Negative Ideal Solution)” is expressed and the concrete steps of hybrid multi-attribute decision making on vague sets is given. Finally, the proposed method is applied into a case study and the result proves the method is effective.