Sensitivity Analysis for Hierarchical Decision ModelsHongyi ChenAbstract
In this dissertation, a comprehensive algorithm is developed to analyze the sensitivity of hierarchical decision models (HDM), which include the well-known analytic hierarchy process (AHP) and its variants, to single and multiple changes in the local contribution matrices at any level of the decision hierarchy. The algorithm is applicable to all HDM that use an additive function to derive the overall contribution vector. It is independent of pairwise comparison scales, judgment quantification techniques and group opinion combining methods. The direct impact of changes to a local contribution value on decision alternatives’ overall contributions, allowable range/region of perturbations, contribution tolerance, operating point sensitivity coefficient, total sensitivity coefficient and the most critical decision element at a certain level are defined by five groups of theorems and corollaries and two groups of propositions in the HDM SA algorithm. Two examples are presented to demonstrate the applications of the HDM SA algorithm on technology evaluation and energy portfolio forecast. Significant insights gained by the two applications demonstrate the contributions of the algorithm. Theorems and corollaries in the HDM SA algorithm were verified and validated by data from the two application models.
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