Correlated Analytic Hierarchy Process

The analytic hierarchy process (AHP) has been the most popular tool for the field of decision making in the past 30 years, because of its simplicity and rationality. Construct a hierarchy system for evaluation by decision makers. Hence, only the effect of outer-dependence can be considered in the AHP. However, besides outer-dependence, correlation is another common effect between criteria which cannot be accounted for neither by the AHP nor by the analytic network process (ANP). Hence, in this paper, we extend the AHP to consider the correlation effect. In addition, a biobjective programming model is proposed to derive the result. Furthermore, the traditional AHP can be considered as the special case of the proposed model when the correlation effect between criteria is ignored. Finally, a numerical example is given to justify the proposed method and compare the result with the AHP.