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 case 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. (C) 2005 Elsevier Ltd. All rights reserved.