On the hierarchical model PCbHA: a more general case

The PCbHA is a rank preserved hierarchical decision model which comes from the weighted mean. This paper considers a more general case of this model where the sub-criteria can have more than one dominating criteria. We first show that this generalized PCbHA also originates from the weighted mean but in a more general way. We then prove the rank preservation property of the generalized model. Comparisons of the model with some existing models (mainly with the AHP and the multiplicative AHP) are also conducted. The result in this paper ensures the PCbHA’s adaptability to more practical needs.