par Doignon, Jean-Paul 
;Falmagne, Jean-Claude
Référence Journal of mathematical psychology, 11, 4, page (473-499)
Publication Publié, 1974-11
;Falmagne, Jean-Claude Référence Journal of mathematical psychology, 11, 4, page (473-499)
Publication Publié, 1974-11
Article révisé par les pairs
| Résumé : | Let A, B be two sets, with B ⊂ A × A, and ≤ a binary relation on B. The problem analyzed here is that of the existence of a mapping u: A → R, satisfying: (a,b) ℓ (a ́,b ́) iff ∨∧ μ(b) - μ(a) ≤ μ(b ́) - μ(a ́) whenever (a, b), (a′, b′) ∈ B. In earlier discussions of this problem, it is usually assumed that B is connected on A. Here, we only assume that B satisfies a certain convexity property. The resulting system provides an appropriate axiomatization of Fechner's scaling procedures. The independence of axioms is discussed. A more general representation is also analyzed: (a,b) ℓ (a ́,b ́) iff ∨∧ F[μ(b), μ(a)] ≤ F[μb ́], where F is strictly increasing in the first argument, and strictly decreasing in the second. Sufficient conditions are presented, and a proof of the representation theorem is given. © 1974. |
