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On a linear functional equation with a mean-type mapping having no fixed points

Katarzyna Sajbura (2005)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Our aim is to study continuous solutions φ of the classical linear iterative equation φ(f(x,y)) = g(x,y)φ(x,y) + h(x,y), where the given function f is defined as a pair of means. We are interested in the case when f has no fixed points. In turns out that in such a case continuous solutions of (1) depend on an arbitrary function.

On a new class of distances between fuzzy numbers.

Carlo Bertoluzza, Norberto Corral, Antonia Salas (1995)

Mathware and Soft Computing

In the course of the studies on fuzzy regression analysis, we encountered the problem of introducing a distance between fuzzy numbers, which replaces the classical (x - y)2 on the real line. Our proposal is to compute such a function as a suitable weighted mean of the distances between the α-cuts of the fuzzy numbers. The main difficulty is concerned with the definition of the distance between intervals, since the current definitions present some disadvantages which are undesirable in our context....

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