Integration of the sensitivity analysis and consistency analysison the decision making region
一种灵敏度和一致性相结合的决策区域分析

The effect of the value of one entry of the comparison matrix on the priority stabilization and consistency ratio in the Analytical Hierarchy Process (AHP) is studied.First,based on the conclusion of the negative correlation between the principal eigenvalue and the coefficient of degree n-3 of the characteristic polynomial of the comparison matrix,the optimization value of the entry that keeps the matrix having the minimum consistency ratio was obtained.The consistency ratio monotonously decreased to the left side of the optimization value,while it monotonously increased to the right side.Second,an iteration algorithm was suggested to find the changeable range of the entry that keeps the matrix having the satisfactory consistency.Third,a decision making region that guaranteed the ranking of the alternative and keeps the matrix having the satisfactory consistency was obtained.Finally,an example was given to illustrate the approach.