Weight sensitivity measurement based on vector analysis in multi-attribute evaluation

Weights is used to measure the relative importance of multiple attributes or objectives, which influences the evaluation or decision result to a great degree. Thus weight sensitivity analysis is an important work in decision-making. An analysis method based on comparison of inclined angles of vectors has been proposed in order to solve the sensitivity of a multiattribute evaluation with isotonicity characteristic. This method uses the cosine of inclined angles to measure the weight sensitivity based on preferences or preference combinations. The concept of sensitivity degree and the relevant algorithm are proposed, and rationality of this algorithm is also proved. Also, this method is used to analyze the solutions of the water environment protection project in Heyuan City.