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

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

[学科分类] 自然科学（综合）