Scale Sensitivity and Rank Preservation

Part of the Applied Optimization book series (APOP, volume 29)


In the previous chapters we have extensively used a geometric scale in order to model the gradations of comparative human judgement. Geometric progression seems to be reasonable but the progression factor 2 established on the basis of the categorization of time, space, light, and sound, remains questionable. The present chapter is therefore concerned with a one-parameric class of geometric scales. We analyze the behaviour of the AHP and SMART when the so-called scale parameter varies over a positive range of values. Theoretical arguments and numerical experiments with small and large problems show that the scale sensitivity of the terminal scores is low whereas the rank order remains unchanged.


Rank Preservation Criterion Weight Impact Score Comparative Judgement Judgement Aggregation 
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© Kluwer Academic Publishers 1999

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