A probabilistic theory of measurement

In this paper we propose a complete probabilistic theory of measurement.This theory includes a probabilistic representation for order, interval and ratio scales and a probabilistic description of the measuring system and of the measurement process.For ease of illustration, a deterministic theory of the ideal measurement is presented first, then its probabilistic counterpart is developed.A full set of proofs is included in which the set of objects—which manifest the quantity to be measured—is finite.