Numerical scaling of ratio scale utilities in multi-criteria decision analysis with geometric model

The ratio scale measurement of utilities in multi-criteria decision analysis has been criticised due to theoretical and practical interpretation of the required assessments. Compared to the ratio scale models, for example, the '0-1-scale' models based on interval scale have been more generally accepted. On the other hand, under some conditions it has been shown that the results of multi-criteria decision support based on ratio scale comparisons are actually independent of the numerical magnitude of the ratio scale assessments. This paper reviews and interprets these results and proposes new solutions for the remaining problems, for which the numerical magnitude of the ratio scale utilities is required. Moreover, we interpret the scale-independent ratio scale models with respect to some other multi-criteria decision support models. The theoretical analysis is carried out by statistical models and illustrated by numerical examples.