Using this scale, comparisons can yield only values between one and nine, or their reciprocals (which apply where an element is of lesser importance than the other element). A more detailed scale is not regarded as meaningful. This scale has the advantage of converting verbal comparisons into numerical values, so that measurability on a relational scale is possible. 6-4: Saaty's nine-point scale for pair comparisons The maximum difference of importance between two elements.įig. The very much greater importance of one element in comparison with the other element has been shown clearly in the past. An infinite relative importance would mean the target criteria or alternatives regarded were not comparable, and a renewed target and problem analysis would be required.įor the pair comparisons, the nine-point scale suggested by Saaty (1980) and illustrated in Figure 6-4 may be used.īoth compared elements have the same importance for the next higher element.Įxperience and estimation suggest a slightly greater importance of one element in comparison with the other element.Įxperience and estimation suggest a considerably greater importance of one element in comparison with the other element. Moreover, a comparative value vic should never be infinite. Then, for an element at the next level up it applies: That is, the comparative value of i relative to c must equal the reciprocal of the comparison between c and i. Reciprocity should apply for the estimated values. This will indicate, for an element at the next level up, the relative importance of i and c, and must be estimated for all elements of the higher level and for all levels. With regard to the pair comparisons, it is assumed that the decision-maker is able to determine values vic for all pairs i and c from the set A (target criteria or alternatives) on a relational scale. For alternative investment projects, this relative importance represents a degree of profitability. Thus, each element's relative importance for fulfilling target criteria is ranked at each level, as a contribution to the fulfilment of the overall target. This is done using pair comparisons with other elements at the same level. This involves estimating and quantifying the relative importance of every element in relation to each element of the hierarchy immediately above. The second step is the determination of priorities for all elements of the hierarchy. The measurability of target criteria has not to be considered in this step of the AHP. Usually, it is also assumed that all relevant alternatives and target measures will be considered. Finally, assessments should be independent of other assessments at the same and other levels. In addition, the elements of a single level should be comparable and belong to the same category of importance. This implies that no (or only minor) relationships exist between the elements of a single level. Relevant relationships should exist between the elements of successive levels only. In this step, an unambiguous demarcation must be drawn between different alternatives and sub-targets. The initial formation of the hierarchy requires segmentation and hierarchical structuring of the decision problem. Evaluation of the subjective priority assessments for consistency is another characteristic feature of the method. Under certain circumstances some of these steps must be repeated, particularly where priority estimations are inconsistent. Determination of (global) priorities for the sub-targets and alternatives with respect to the whole hierarchy.
Examination of the consistency of the priority assessments.ĥ.
Calculation of local priority vectors (weighting factors).Ĥ. The AHP is carried out using the following steps:ģ. Then, a total value is calculated for subtargets to determine their relative importance for the whole hierarchy, and, ultimately, to assess the overall profitability of the alternative investment projects. In each case, the relative importance (weightings) of the different criteria, and the relative profitability of alternatives, is determined with respect to each element of the higher level by using pair comparisons. Using the AHP, both qualitative and quantitative criteria can be considered. At the lowest level(s) of the hierarchy, the alternatives (here, the investment projects) are included. A hierarchy containing multiple target levels, such that the main target is broken down into sub-targets. The AHP splits the decision process into partial problems in order to structure and simplify it. One important application of the method is the support of decision-making involving multiple objectives. The analytic hierarchy process (AHP) was developed by Saaty (1980) in the early 1970s to structure and analyse complex decisions.
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