Technique for Order Preference by Similarity to Ideal Solution(TOPSIS) Applied in Vague Sets

Technique for order preference by similarity to ideal solution(TOPSIS),whose attribute value and weight are Vague sets,is brought into Vague sets.Attribute value is weighted according to addition and multiplication of Vague sets.Positive and negative ideal solutions are based on Score function.The distance of both positive and negative metrics is defined the Hausdorff metrics based on Vague sets,thus developing the TOPSIS methods based on Vague sets.It is finally verified effectively by a case.