Abstract
The idea of a fuzzy functional equation of the type
Y =
f(
X
1,
X
2,…,
X
n
,
A
1,
A
2,…,
A
s
) (where
X
1,
X
2,…,
X
n
,
A
1,
A
2,…,
A
s
are treated as fuzzy numbers) and the methods of its resolution are dealt with. It is shown that in the case of existence of
A
1,
A
2,…,
A
s
, satisfying the equation given above, the resolution problem is equivalent to the resolution of fuzzy relational equation of the type
Y=A
1∘A
2∘⋯∘A
s∘R
The idea of fuzzy functional equations generated by fuzzy relation is presented and the algorithm using the notion of probabilistic sets and leading to the resolution of fuzzy functional equations in the case of “noises” is given as well. Some numerical examples form an illustration of presented algorithms, pointing out there, the most characteristic features.