SMM11 — Scales of Measurement

A standard component of measurement theory is 'Scales of Measurement' because they constrain the types of mathematical operations that can be performed on a measure. The base set of scales are 'Nominal', 'Ordinal', 'Interval', and 'Ratio'. The representation of a measure in SMM should contain information about the scale of measurement to indicate how it can be used and the limits of the operations that can be performed. If there is a way to enforce these constraints that would be best, but lacking that it would be useful for the specification of a measure to contain information about its limits for those who would incorporate the measure in their applications.

Add scaleOfMeasurement property to Measure, with enumerated type, consisting of the following five enumeration values: the four standard ones, namely “nominal”, “ordinal”, “interval”, and “ratio”, and the fifth being “custom”. In case of “custom”, the Measure has another string property instantiated, representing the custom scale (e.g. Guttman). In addition, add a few constraints, like: allow nominal & ordinal on GradeMeasure, and allow interval & ratio on DimensionalMeasure.