On weighted synthesis of judgements (Q796423)

The problems connected to synthesizing judgements [see the author and \textit{T. J. Saaty}, J. Math. Psychol. 27, 93-102 (1983; Zbl 0522.92028) and the author and \textit{C. Alsina}, Methods Oper. Res. 48, 3-22 (1984; Zbl 0527.39002)] are solved here in the nonsymmetric case where the synthesizing function is \(f(x_ 1,...,x_ n)=g_ 1(x_ 1)\circ...\circ g_ n(x_ n).\) The results are reasonably similar to the symmetric case and so are the conditions except that cancellativity is replaced by the local sensitivity (or partial philandering) property of f which states in this case that \(x_ k\mapsto f(x_ 1,...x_ k,...,x_ n)\) has no constant interval \((k=1,...,n)\).