The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation

a₁ a₁₁ activities actors allocation alternatives Amax analysis Analytic Hierarchy Process approach binary matrix C₁ clusters coefficients compared complete graph components composite considered consistency corresponding cost criteria defined Delphi method denote derived desired future diagonal directed graph dominance eigenvalue problem eigenvector elements entries equal equation estimate example forward process given gives goal graph hence hierarchy level impact importance influence irreducible judgments left eigenvector linear measurement method multiple nonnegative normalized objectives obtain outcome overall pairwise comparison perturbation policies positive preferred primitive matrix priority vector projects PROOF properties rank ratio scale reciprocal matrix relations relative respect result right eigenvector root mean square row sums scenario social solution stochastic matrix structure Sudan supermatrix Table theorem theory utility function v₁ variables vertex vertices w₁ w₁/w weights x₁ zero λ₁