Abstract
Recently the analytic hierarchy process (AHP) developed by T.L. Saaty attracts attention as one of the particularly useful vehicles for allocating resources, analyzing policy impacts, and making a decision.
This paper presents some useful theorems for the sensitivity analyses of priorities (i.e., relative importances) used in the AHP. These theorems are derived from the principle of hierarchical composition which is expressed in the form of reachability matrix. Using the theorems, we can easily calculate the degree of effects caused by local or global changes in the priorities of some criteria, and also we can examine about the possibility of rank reversal among alternatives.
This paper, also, presents an application of the theorems to the problem of house selection, and demonstrates their effectiveness.
