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THE SUPERMATRIX EIGENPROBLEM: AN INTERPRETATION OF THE PRIORITY VECTORS IN THE ANALYTIC NETWORK PROCESS

Stan Lipovetsky

Abstract


Continuing the previous articles on interpretation of the solutions obtained in the Analytic Hierarchy Process (AHP) and in the Analytic Network Process (ANP) with outer dependence, the current work considers a general ANP problem and shows that the solution for its supermatrix, obtained by raising the supermatrix to powers is equivalent to solving the eigenproblem for this matrix. Thus, the global priority solution for an ANP model is an eigenproblem of its supermatrix, and the principal eigenvector of the supermatrix itself gives the mean priorities for the whole network of the compared items. This approach provides an easy way to describe complex ANP interconnections, and gives an explicit interpretation of the priority results convenient for practical managerial decisions.

http://dx.doi.org/10.13033/ijahp.v5i1.132


Keywords


Analytic Network Process, Supermatrix Eigenvectors

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DOI: http://dx.doi.org/10.13033/ijahp.v5i1.132