Journal of Applied Mathematics and Decision Sciences 
Volume 2 (1998), Issue 2, Pages 147-158
doi:10.1155/S117391269800008X

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

Abstract

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.