Editing Measurement (section)

=== Representational theory ===
In the representational theory, ''measurement'' is defined as "the correlation of numbers with entities that are not numbers".<ref>Ernest Nagel: "Measurement", Erkenntnis, Volume 2, Number 1 / December 1931, pp.&nbsp;313–335, published by [[Axel Springer AG|Springer]], the Netherlands</ref> The most technically elaborated form of representational theory is also known as [[additive conjoint measurement]]. In this form of representational theory, numbers are assigned based on correspondences or similarities between the structure of number systems and the structure of qualitative systems. A property is quantitative if such structural similarities can be established. In weaker forms of representational theory, such as that implicit within the work of [[Stanley Smith Stevens]],<ref>Stevens, S.S. ''On the theory of scales and measurement'' 1946. Science. 103, 677–80.</ref> numbers need only be assigned according to a rule.

The concept of measurement is often misunderstood as merely the assignment of a value, but it is possible to assign a value in a way that is not a measurement in terms of the requirements of additive conjoint measurement.  One may assign a value to a person's height, but unless it can be established that there is a correlation between measurements of height and empirical relations, it is not a measurement according to additive conjoint measurement theory. Likewise, computing and assigning arbitrary values, like the "book value" of an asset in accounting, is not a measurement because it does not satisfy the necessary criteria.

Three type of representational theory
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#; Empirical relation : In science, an ''empirical relationship'' is a relationship or correlation based solely on [[observation]] rather than theory. An empirical relationship requires only confirmatory data irrespective of theoretical basis.
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#; The rule of mapping : The real world is the Domain of mapping, and the mathematical world is the range. when we map the attribute to mathematical system, we have many choice for mapping and the range.
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#; The representation condition of measurement :