Translating Discrete Estimates into a Less Detailed Scale: An Optimal Approach

Thongchai Dumrongpokaphan, Olga Kosheleva, Vladik Kreinovich

Abstract

In many practicalsituations, we use estimates that experts make on a 0-to-$n$scale. For example, to estimate the quality of a lecturer, we askeach student to evaluate this quality by selecting an integer from0 to $n$. Each such estimate may be subjective; so, to increasethe estimates' reliability, it is desirable to combine severalestimates of the corresponding quality. Sometimes, differentestimators use slightly different scales: e.g., one estimator usesa scale from 0 to $n+1$, and another estimator uses a scale from 0to $n$. In such situations, it is desirable to translate theseestimates to the same scale