Measurement, Representational Theory of

Abstract

The principles of representational measurement theory are expounded in historical and contemporary perspective, including a preliminary formulation of representation, uniqueness, and meaningfulness. The whole article is based on the concept of an ordered relational structure. The definition and representation theorems of extensive and difference structures are presented and discussed. These are ordered relational structures with operations or difference-like relations defined on them. Stevens's classification of scale type (i.e., the classical ratio, interval and ordinal scales) and its modern development in the context of the automorphism group of a measurement structure are dealt with, leading naturally to the problem of meaningfulness of numerical statements. Finally problems and applications of the representational theory of measurement are pointed out.