Weight sensitivity measurement, analysis, and application in multi-attribute evaluation

Abstract

Weights are used to measure relative importance of multiple attributes or objectives, which influence evaluation or decision results to a great degree. Thus, analyzing weight sensitivity is an important work for a multi-attribute evaluation or decision. A measuring method based on the inclined angle of two vectors is proposed in this paper in order to solve the weight sensitivity of a multi-attribute evaluation with isotonicity characteristic. This method uses the cosine of the inclined angle to measure the weight sensitivity based on preferences or preference combinations. Concepts of sensitivity space, degree, and angle are given, and the relevant measurement method is discussed and proved. Also, this method is used for the choice of the water environment protection projects in Heyuan City.

Keywords:

• sensitivity degree
• multi-attribute evaluation
• inclined angle of vectors

Acknowledgment

This work is supported by the Natural Science Foundation of China (No. 71071063), the National High Technology Research and Development Program of China (863 Program) (No.2009 AA04Z107), and the Science and Technology Bureau of Heyuan City.