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Published in:
2011 | OriginalPaper | Chapter
Solutions of Equation I(x,y) = I(x,I(x,y)) for Implications Derived from Uninorms
Authors : Sebastia Massanet, Joan Torrens
Published in: Fuzzy Logic and Applications
Publisher: Springer Berlin Heidelberg
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Uninorms are one of the most studied classes of aggregation functions and with more applications in the field of the aggregation of information. Their conjunctive or disjunctive behaviour is essential for their use as logical connectives and for obtaining fuzzy implications derived from uninorms. In this communication, we want to analyse which fuzzy implications derived from uninorms satisfy the iterative equation
I
(
x
,
y
) =
I
(
x
,
I
(
x
,
y
)). This equation comes from
p
→
q
≡
p
→ (
p
→
q
), a tautology in classical logic, and it is related with the law of importation respect to the minimum
I(
min
{x,y},z)=I(x,I(y,z))
.