Mayor, G. Sugeno’s negations and \(t\)-norms. (English) Zbl 0821.39005 Mathware Soft Comput. 1, No. 1, 93-98 (1994). A functional characterization of Sugeno’s negations \(N(x) = (1 - x)/(1 + cx)\) \((c > - 1)\) is given by showing that such functions are the only solutions with a fixed point of the equation \(x(y - 1) f(x) + y(1 - x) f(y) = (y - x) f(x) f(y)\).A new characterization of the family of \(t\)-norms \(\text{Max} (0,(1 - p) xy + p(x + y - 1))\) is given. Reviewer: C.Alsina (Barcelona) Cited in 6 Documents MSC: 39B22 Functional equations for real functions Keywords:Archimedean \(t\)-norm; strong negation; functional equation; Sugeno’s negations; fixed point PDFBibTeX XMLCite \textit{G. Mayor}, Mathware Soft Comput. 1, No. 1, 93--98 (1994; Zbl 0821.39005) Full Text: EuDML