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Sugeno’s negations and \(t\)-norms. (English) Zbl 0821.39005

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.

MSC:

39B22 Functional equations for real functions
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