Generalized Analytic Network Process with Path Restriction by the Distance Matrix and Transition Functions

Abstract

The analytic network process (ANP) is a generalized analytic hierarchy process used to handle the interdependency and feedback effects between criteria in various multi-criteria decision-making problems. However, problems regarding the ANP have been proposed because of its restrictions and limitations when used in practice. In this paper, we focus on the issues of path restriction between criteria and the transition functions of the supermatrix. It has been postulated that with regard to path restriction between criteria, a criterion with a longer path to another criterion should have less influence, which is likewise assumed in the conventional ANP. In addition, we add transition functions into the supermatrix to calculate the steady-state weights of the criteria. Transition functions are beneficial because they allow the consideration of the supermatrix’s nonlinear transition instead of the linear situation. The numerical examples in this study show that our proposed method is a generalization of the ANP and reduces to the conventional ANP if the path restriction is released, and the transition function is linear.