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By N. Cooke

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4) is called homomorphism. 2 is a required feature of mapping ????, but does not yet explain how a numerical value quantifying property manifestation q can be assigned to symbol x. To do so, a suitable measurement scale should be defined, through the following steps. 1. A set ΩS = {????Sn } of standard objects is chosen in such a way that it provides a set QS = {qSn } of manifestations of the same property as the measurand. 2. A relation ????S : ΩS → QS is defined between the set of standard manifestations of the property and symbols, so that a set XS = {xSn } of symbols is obtained, corresponding to each standard manifestation, and the representation condition is satisfied.

For this reason, the error concept has been abandoned, and replaced by the more modern concept of uncertainty. 1, the true value of the measurand is unknown and unknowable. Therefore, the task of characterizing the distribution of values that could reasonably be attributed to the measurand is made difficult by the fact that, not knowing the measurand, we cannot know whether the measured values belong to that distribution or not. This means that a more complex mathematical approach than the simple error concept is required to define and handle this problem.

1) that belongs to the symbolical world. In fact, measurement is an objective empirical operation that assigns a symbol x (called the measured value) to the manifestation q (called the measurand) of the considered property of an object [4, 8, 9]. 5 A”, we assign this symbol, whose meaning is assumed to be known, to the current. The above relationship between an empirical property and a symbol can be represented using a mathematical formalism. Consider a generic property and let q1 , q2 , … , qn , … represent single manifestations of that property, so that we can define a set of all possible manifestations as Q = {q1 , q2 , … , qn , …}.

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Allied Electronics Data Handbook by N. Cooke

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