The average of this normed vector gives the average coherence. Then, we divide the latter by the weight of the priority vector of the element of the same line. To obtain the average consistency, we first multiply the comparison matrix with its priority vector, which gives us a new vector. The number of items is the number of columns or rows in the comparison table. The equation for the coherence index is as follows.ĬI = mean coherence – element number / (element number -1) It is measured with 2 parameters: the coherence index (CI) and the coherence ratio (CR). Indeed, if the alternative A1 is evaluated slightly more important (code 2) than the alternative A2, and A2 is judged moderate important (code 3) than the alternative A3 and A3 strong important (code 5) than A1, then the test says that there is a data inconsistency. This test controls the entered values in the comparison tables. We thus obtain the weights of each criterion and subcriterion which are finally used as the weighting in the calculation of alternatives priority vectors with the same mathematical equation given above.Īn option in the output results is proposed to assess the data consistency. This vector is then weighted by the weight of the criterion linked. With the same equation, the priority vector of subcriteria is calculated for each criterion. The weight of each criterion = sum of normalized lines/criteria number the computation of the weight of each criterion.

The first computation of the AHP method is the calculation of the criteria priority vector from the values of the criteria comparison table, i.e. Saaty has defined an evaluation scale that measures the importance or the difference of one element over another one. The comparison tables must be completed by the user according to the values chosen in the table of Saaty (see Help documentation). It is available in the Decision Aid menu under the Advanced features ribbon. XLSTAT proposes the DHP tool to create your own design of experiments. The set of these tables is called the experimental design for an AHP analysis. At level 2 the comparison tables of alternatives over criteria and/or subcriteria must be defined. At level 0 the criteria comparison table must be defined, at level 1 those of subcriteria if it is a level 2 problem, otherwise the comparison tables of alternatives over criteria. There are tables to define at each level of the hierarchy. The principle of the method is to evaluate 2 by 2 the elements of the problem in comparison tables. We talk about a 2-level problem when it admits subcriteria, otherwise, it is a problem of level 1. We denote by alternative the solutions of the decision problem, criteria the parameters on which the alternatives are evaluated, subcriteria the parameters belonging to a criterion and on which alternatives are evaluated and evaluator the person who makes the evaluations. Thomas Saaty is at the origin of this method and created it in the 1970s. The approach of the method is to simplify the problem by breaking it down into a hierarchical system. What is Analytic Hierarchy Process (AHP)?Īnalytic Hierarchy Process is a method adapted to multi-criteria decision problems that have several solutions satisfying a set of criteria.

Ahp decision matrix