数学中国w, madio,net 164 The LAP Journal 29.2(2008) Sensitivity Analysis About the values of the metrics In this part, we change the values but keep the weights to see how can this change affect the evaluation result. Then we can arrive at the most important metric, the one that can affect the final score acutely Suppose that Gp and Ga are the final scores of countries p and g. Let Uor be the the value of metric r in country q. Change it to make G, = Ga;then we can get the marginal value U Uo=Ue+ We can do sensitivity analysis to the values of the metrics following the rocess below If Ug is outside of the allowable interval, whatever it changes, it won't change the order of the two countries; so r is a value- insensitive metric. When Uor is close to U, changing the value will change the order of the two countries, so r is a value- sensitive metric. About the Weights In this part, we change the weights but keep the values of the metrics to see how doing so affects the evaluation result. Then we can get the most important weight, the one that can affect the final score acutely To make a simple analysis, when a weight changes, let only one another change at the same time, and keep the others fixed Suppose that the weights values before they change are ,, U,,, G,and after changing they are w;, Ui, Gr. Suppose that the changing weights are r and 8, so that W,+w,=wr+w The changing interval of and w, is 0, w, +ws. When they change, maybe the final score of one country will equal that of another. Let the two countries be p and g. Then we can get the marginal weights =0-0)=(0-0m5 (m+觉) When the two countries have the same score, we can get r and w, as数学中国 www.madio.net