A fuzzy weight representation for ANP using sensitivity analyses of pairwise comparison.(Session 4a)

Abstract

ANP (Analytic Network Process) was developed from AHP (Analytic Hierarchy Process) with network structure. ANP has been used in the domain of decision making, and is useful for solving problems with network structure or dependency between elements. An eigenvector of a pairwise comparison matrix is often employed as an element of a super matrix in ANP. A sensitivity analysis for a pairwise comparison matrix is proposed, because data often lose their reliability. In other words a comparison matrix does not always have enough consistency. In this case, a fuzzy representation for weights is useful. We propose a fuzzy representation for the components of a super matrix, using the results from the sensitivity analysis. It enables us to find the composite weight of ANP as a fuzzy number when the comparison matrix does not have good consistency.