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Finite equal‐interval measurement structures
Author(s) -
SUPPES PATRICK
Publication year - 1972
Publication title -
theoria
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.34
H-Index - 16
eISSN - 1755-2567
pISSN - 0040-5825
DOI - 10.1111/j.1755-2567.1972.tb00923.x
Subject(s) - interval (graph theory) , citation , computer science , mathematical economics , combinatorics , discrete mathematics , mathematics , library science
In this article I consider some of the simplest non-trivial examples of measurement structures. The basic sets of objects or stimuli will in all cases be finite, and the adequacy of the elementary axioms for various structures depend heavily on this finiteness. In addition to their finiteness, the distinguishing characteristic of the structures considered is that the objects are equally spaced in an appropriate sense along the continuum, so to speak, of the property being measured. The restrictions of finiteness and equal spacing enormously simplify the mathematics of measurement, but it is fortunately not the case that the simplification is ac- companied by a total separation from realistic empirical applica- tions. Finiteness and equal spacing are characteristic properties of . many standard scales, for example, the ordinary ruler, the set of standard weights used with an equal-arm balance in the laboratory or shop, or almost any of the familiar gauges for measuring pressure, temperature, or volume. Four kinds of such structures are dealt with, and each of them corresponds to a more general set of structures analyzed in the comprehensive treatise of Krantz, Luce, Suppes and Tversky (1971). The four kinds of structures are for extensive, difference, bisection, and conjoint measurement.