János Aczél, Günter Rote, and Jens Schwaiger:
1. Webs, iteration groups, and equivalent changes in probabilities
1a. In: “VIII. Mathematikertreffen Zagreb-Graz”, Universität Graz,
9.-11. 12. 1993. Editors: Detlef Gronau and Ludwig Reich. Grazer
Mathematische Berichte 323, 1994, pp. 1–20, (Zbl 816.39003).
1b. Quarterly of Applied Mathematics 54 (1996),
475–499, (Zbl 859.39010).
2. Equivalence of changes in proportions at crossroads of mathematical
theories
2a. In: “Actes 5eConférence Internationale/Proc. Fifth International
Conference IPMU, Traitement d'information et gestion d'incertitutes dans les
systèmes à base de connaissances/Information Processing and
Management of Incertainty in Knowledge-Based Systems, Paris, 4–8 juillet/July,
1994, Cité Internationale Universitaire”, Paris 1994, Vol. 1,
pp. 569–570.
2b. In: The Ordered Weighted Averaging Operators — Theory and Applications.
Editors: Ronald R. Yager and Janusz Kacprzyk, Elsevier, Dordrecht 1997,
pp. 36–38.
Abstract
Yew-Kwang Ng (Quart. Appl. Math. 49 (1991), 289--301) listed several
“reasonable properties” for equivalent changes of
probabilities and other proportions. He produced a family of
functions satisfying all properties and asked whether there exist
essentially different ones, conjecturing that the answer is negative.
We show that the answer is positive, by constructing uncountably many
families of functions satisfying all properties. We show also that
there are no other solutions. Our method establishes connections with
webs (nets) and iteration groups. This may be of interest both in
itself and for applications.
Last update: August 16, 2004.