Incorporating the uncertainty of decision judgements in the Analytic Hierarchy Process

The uncertainty in the relative weights of a pairwise comparison matrix in the Analytic Hierarchy Process (AHP) is caused by the uncertainty in our decision judgements and in many cases can not be avoided. In this paper, it is explicitly shown how such uncertainties can be incorporated within the framework of AHP and how the resulting uncertainties in the relative priorities of the decision alternatives can be computed. The required algorithm and the computational procedures are also developed and illustrated with examples. Uncertainty is introduced as a fundamental concept independent of the concept of consistency with a view to extend the AHP as a decision analysis procedure.