Exact measurement is a mapping f 0 from the structure of physical objects into the structure of real numbers R representing the results of measurement. In the framework of the fuzzy theory of measurement an inexact measurement is represented by a mapping f from a physical objects into a structure of fuzzy intervals. The paper is devoted to the study of properties of mapping γ from fuzzy intervals into real numbers which describe the relation between the exact f 0 and inexact f measurement. We assume that the mapping γ is R representation of fuzzy intervals (named the measurement defuzzyficator), next it is shown that the mapping γ is linear in relation to the decomposition (in the arithmetic based on t-norm) of fuzzy intervals into components of fuzzy numbers representing components of inexactness (systematic and random) and exact values.