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.
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