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Zbl 1226.91049
Luce, R.Duncan; Narens, Louis
Measurement scales on the continuum. (English)
[J] Science 235, No. 4808, 1527-1532 (1987). ISSN 0036-8075

Summary: In a seminal article, {\it S. S. Stevens} [Science 103, No. 2684, 677--680 (1946; Zbl 1226.91050)] noted that the numerical measures then in common use exhibited three admissible groups of transformations: similarity, affine, and monotonic. Until recently, it was unclear what other scale types are possible. For situations on the continuum that are homogeneous (that is, objects are not distinguishable by their properties), the possibilities are essentially these three plus another type lying between the first two. These types lead to clearly described classes of structures that can, in principle, be incorporated into the classical structure of physical units. Such results, along with characterizations of important special cases, are potentially useful in the behavioral and social sciences.

MSC 2000:: *91C05 Measurement theory

Citations: Zbl 1226.91050

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