A unified model and analysis for the analytic hierarchy process and analytic network process

Saaty proposes the analyzing methods for AHP using the principal eigenvector of the comparison matrix, and for ANP using the limiting process method of the powers of the supermatrix. These methods are based on the irreducibility of the evaluation matrices. We develop the unified method solving both AHP and ANP based on Frobenius min–max theorem. Further this method is extended to the solving method of the general (not necessarily irreducible) evaluation matrix, by the graphic decomposition process.