Additive representation for equally spaced structures
type: Item
instance of: scholarly article
title: Additive representation for equally spaced structures
zbMATH Open document ID: 0731.92031
DOI: 10.1016/0022-2496(91)90028-R
published in: Journal of Mathematical Psychology
publication date: 1991-01-01T00:00:00Z
review text: The author shows that in the equally spaced discrete case of additive conjoint measurement a simple necessary and sufficient condition can be given. The approach is similar to that of \textit{D. H. Krantz, R. D. Luce, P. Suppes} and \textit{A. Tversky} [Foundations of measurement (1971; Zbl 0232.02040)] and uses assumptions of restricted solvability, coordinate independence, an Archimedean axiom, a discreteness condition called the equally spaced condition, and the weak separability condition that for all i, x, y, \(v_ i\), \(w_ i:\) \[ x_{-i}v_ i\succcurlyeq x_{- i}w_ i\quad if\text{ and } only\quad if\quad y_{-i}v_ i\succcurlyeq y_{-i}w_ i. \] The range of each additive value function is then an interval of integers.
Mathematics Subject Classification ID: 91C05
Mathematics Subject Classification ID: 91E45
zbMATH DE Number: 4209945
zbMATH Keywords: discrete case of additive conjoint measurement
zbMATH Keywords: restricted solvability
zbMATH Keywords: coordinate independence
zbMATH Keywords: Archimedean axiom
zbMATH Keywords: equally spaced condition
zbMATH Keywords: weak separability condition
zbMATH Keywords: additive value function
author: Peter P. Wakker
reviewed by: Ki Hang Kim
MaRDI profile type: Publication
cites work: Q5663601
cites work: Difference measurement and simple scalability with restricted solvability
cites work: Unique finite conjoint measurement
cites work: On the extension of additive utilities to infinite sets
cites work: Q5639713
cites work: The algebraic versus the topological approach to additive representations
cites work: Q3994760
full work available at URL: 0022-2496(91)90028-r
OpenAlex ID: W2135246652
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description: scientific article; zbMATH DE number 4209945