#Analytic hierarchy process 3 levels how to
#Analytic hierarchy process 3 levels Pc

The product of the MPSC matrix and the MPASC matrix gives the PAC matrix of priorities of the alternatives in each criterion, shown in rows 36–39. In turn, the subcriteria vectors are grouped into a partitioned MPSC matrix to match the rows of the MPASC matrix. The vectors of priorities of each alternative in each subcriterion are sorted and grouped in the MPASC matrix.

#Analytic hierarchy process 3 levels Pc

One then calculates the PSC1 and PSC2 priorities of each subcriterion for each criterion and the priorities of each criterion for the final objective in the PC vector. ĪHP-express process in an Excel spreadsheet.įirst, the priority is calculated for each alternative in each subcriterion SC11, SC12, SC21 and SC22. and in practical situations as reported by do Nascimento Vieira and Leal and Nunes and Leal.

The method has been applied and validated in the literature as presented by Mendes et al.

#Analytic hierarchy process 3 levels how to

Appendix A1 of the supplementary material shows approximate methods for estimating the vector of priorities and how to test the inconsistency of the evaluation matrix. Consequently, Saaty defined how to compute an inconsistency indicator from an array of evaluations and described a test with a parameter to check whether evaluation inconsistency is acceptable. When making multiple comparisons, inconsistencies typically occur that are acceptable within certain limits. The priorities of the criteria are used as weights to calculate the priorities of the alternatives in each criterion until the priorities of the alternatives against the overall objective have been calculated.Īccording to the method proposed by Saaty, given relation 1 and the fact that the diagonal a ij = 1, (n 2 -n)/2 comparisons are made before proceeding with the calculations of priorities for each matrix with n alternatives. The comparison is made by assembling matrices in the same way and with the same scale as presented in Table 1. Finally, each criterion of the first level is compared against the objective. Pairwise comparisons are performed using the method described by Saaty at the fundamental scale presented in Table 1.Ĭomparisons are made between each alternative against each criterion and between each criterion at one level against the higher-level criterion to which it is associated. At a lower level, the alternatives are listed and then compared pairwise according to their contribution to reaching each objective, or criterion, from the lower level. These partial objectives are treated as criteria in this text. Each partial objective at the second level can be decomposed into third-level objectives, and each set at each level meets the objective of the level to which they are subordinate. Partial objectives that meet the main objective are placed at the second level. The method starts by structuring a decision-making problem as a hierarchy in the form of an upside-down tree where the main goal is placed on top. It is suggested that the element taken as a basis is one of apparently greater importance-one whose inconsistency of evaluation would be expected to be the least likely in an application of the complete method. Therefore, assuming evaluation consistency by decisionmakers, a method that reduces the number of comparisons for each criterion or between criteria is proposed, in which comparisons are made only between one element and all other elements. This condition hampers its application to the most important issues, which involve the participation of senior executives in organizations. Interested readers can find a brief discussion on AHP applications in the supplementary material.ĭespite its wide applicability, the AHP method suffers from a notable drawback: it requires a very large number of comparisons to make a decision. have applied this new AHP approach in their work. Recent approaches have combined AHP with other methods as presented by Ahn.

AHP has also been applied to supplier and vendor selection according to Tam and Tummala, Deng et al. and Jadhav and Sonar noted that AHP is the most widely used method for evaluating software. Such values can be used to classify and select alternatives based on a hierarchical structure. , the AHP method makes it possible to assign a value representing the preference degree for a given alternative to each additional alternative. The analytic hierarchy method (AHP), developed by Saaty, is a powerful multicriteria decision-making tool that has been used in numerous applications in various fields of economics, politics and engineering.Īccording to Chai et al.