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.


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.

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Last update: August 16, 2004.