New evaluation method for imperfect alternative matrix

Abstract

In the presumption of the missing values for the imperfect alternative matrix, there are two methods; the Harker method and the Nishizawa method. However, it is often difficult to determine which method is appropriate. This paper focuses on the decision-making process of the Analytical Network Process (ANP) by examining the evaluation matrix as an imperfect matrix. The proposed method is composed of the alternative matrix and the criterion matrix, which is based on the matrix inverse of the alternative matrix, and presumes the missing values in the four by four matrix from the eigenvector. The same estimate obtained by the Harker method is stably obtained by artificially providing information in the imperfect matrix. Furthermore, the essence of the decision-making is considered through these examination processes. © 2011 Springer-Verlag Berlin Heidelberg.