Measurement

The basic idea of measurement is that objects exhibit an attribute for which questions like “do objects exhibit the attribute to the same degree or for any pair of them does one exhibit it more or less than the other?” make sense. It implies ordering objects that show an equal, a greater or lesser amount of one attribute, The notion of order is captured by the concept of a binary relation that is at least a weak order. Stevens (1946, 1951) classified four types of scales through which the assignment of objects to numbers can be achieved. These two approaches converge on the Representational Theory of Measurement, according to which it is the construction of functions from a set of data to a set of numbers, which map the structure they both share (isomorphism). In metrology, models are built to account for the interaction of what is measured with measurement instruments and the environment.