EUDML

The distributivity law for a fuzzy implication $I : {[0, 1]}^{2} \to [0, 1]$ with respect to a fuzzy disjunction $S : {[0, 1]}^{2} \to [0, 1]$ states that the functional equation $I (x, S (y, z)) = S (I (x, y), I (x, z))$ is satisfied for all pairs $(x, y)$ from the unit square. To compare some results obtained while solving this equation in various classes of fuzzy implications, Wanda Niemyska has reduced the problem to the study of the following two functional equations: $h (min (x g (y), 1)) = min (h (x) + h (x y), 1)$ , $x \in (0, 1)$ , $y \in (0, 1]$ , and $h (x g (y)) = h (x) + h (x y)$ , $x, y \in (0, \infty)$ , in the class of increasing bijections $h : [0, 1] \to [0, 1]$ with an increasing function $g : (0, 1] \to [1, \infty)$ and in the class of monotonic bijections...

Page 1

Download Results (CSV)

Advanced Search

Formula preview

Currently displaying 1 – 9 of 9

On discontinuous additive functions

On the mutual noncompatibility of homogeneous analytic non-power mean. (Summary).

On the mutual noncompatibility of homogeneous analytic non-power means.

On permutations involving pairs of twins.

A very elementary proof of a probabilistic limit relation.

A generalization of Steinhaus' theorem to coordinatewise measure preserving binary transformations

Differentiation of implicit functions and Steinhaus' theorem in topological measure spaces

On a problem of E. Michael concerning topological divisors of zero

On two functional equations connected with distributivity of fuzzy implications