AHP Consensus Word Scale

To make the results easier to interpret, we define a descriptive word scale for the consensus range from zero to unity. For this we analyzed the consensus within 140 hierarchy nodes (a set of criteria or sub-criteria within a decision hierarchy) of 35 AHP group decision projects. It could be shown (Fig. 1) that the consensus SAHP is normal distributed with a mean value of 64 % ± 3 %. With a 99.5% probability the consensus of all projects lies between 28 % and 99 %. Therefore we divided the range of the scale in four equal segments from 50 % to 100 % (going from ‘low’ to ‘very high’), and defined the consensus for values below 50 % as ‘very low’.

Table 1 Qualitative wording scale for AHP consensus indicator

Consensus SAHP  < 0.50.5 – 0.6250.625 – 0.750. 75 – 0.87.5> 0.875
Word ScaleVery lowlowmoderatehighVery high

Switching from the consensus indicator SAHP to the relative homogeneity S shifts the mean value from 64 % to 70 %, which can be explained by the fact that in AHP we have a limited 1 to 9 scale and Hα,min is a function of the maximum scale value.

Figure 1 Distribution of consensus SAHP in blue actual values, in red normal distribution
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