A Correct Approach on Adding Criteria in the Analytic Hierarchy Process

This paper deals with addition besides deletion of indifferent or wash criteria on which the alternatives have equal performance in the Analytic Hierarchy Process (AHP) against the misguided argument as shortcoming of the AHP. In such case, it is noted that careful attention and a correct approach are required in order not to be led towards a wrong decision with rank reversal when composing priorities of criteria and performances of alternatives according to the criteria. Contrasting with the case of alternatives, prioritizing added or deleted indifferent criteria requires consistency with the change of conceptual definition in regards to the related elements as well as that of the hierarchical structure if needed. Corresponding to such importance in ranking alternatives, two principles of the AHP need to be considered simultaneously: the completeness of expectation axiom and the outer dependency (hierarchical independence) axiom on which the argument of rank reversal focuses only. It is shown that the Analytic Network Process (ANP) as a general approach can cover the case adding feedback or inner dependency to the given hierarchic relation of criteria. Finally, this paper presents the way in which there is no irrational/unreasonable rank reversal with simple addition of indifferent criteria in addition to the deletion of wash criteria, which helps AHP/ANP application.