Journal of Applied Mathematics and Decision Sciences
Volume 2 (1998), Issue 2, Pages 147-158

On the equiponderate equation xa+xb+x=xc+xd+1 and a representation of weight quadruplets

Bernard de Baets and Hans de Meyer

Department of Applied Mathematics and Computer Science, University of Gent, Krijgslaan 281 (S9), Gent B-9000, Belgium

Copyright © 1998 Bernard de Baets and Hans de Meyer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The equation xa+xb+x=xc+xd+1 considered in this paper is a particular equiponderate equation. The number and location of the roots (w.r.t. x = 1) of this equation are determined in case (a,b,c,d)]0,1[4. Based on these results, it is shown that any weight quadruplet, a basic tool in fuzzy preference modelling, admits an interesting expression in terms of Frank t-norms with reciprocal parameters.