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

a₁ activities allocation alternatives Amax analysis Analytic Hierarchy Process applications approach b₁ binary matrix C₁ clusters coefficients column vector compared complete graph components composite consistency corresponding cost criteria D₁ decision defined denote derived determine diagonal directed graph dominance edges eigenvalue problem elements entries equal equation estimate example factors given gives goal graph hence hierarchy level impact importance influence irreducible judgments least squares left eigenvector linear mathematical measurement method Multidimensional Scaling multiple nonnegative normalized Note objectives obtain outcome overall pairwise comparison pairwise comparison matrix perturbation positive primitive matrix priority vector PROOF rank ratio scale reciprocal matrix relations relative respect result right eigenvector root mean square row sums scenario solution stochastic matrix structure Sudan supermatrix Table Theorem theory unity utility function v₁ variables vertex vertices w₁ weights zero