Fuzzy measurement theory

Exact measurement is a mapping f0 from the structure of physical objects into the structure of real numbers RR 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 f0 and inexact f measurement. We assume that the mapping γ   is RR 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.