Some questions about Zadeh's extension on metric spaces
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https://doi.org/10.1016/j.fss.2018.10.019 |
Metadatos
Título
Some questions about Zadeh's extension on metric spacesFecha de publicación
2018-10-29Editor
ElsevierCita bibliográfica
JARDÓN, Daniel; SÁNCHEZ, Iván; SANCHIS LÓPEZ, Manuel (2018). Some questions about Zadeh's extension on metric spaces.Fuzzy Sets and Systems, online 29 October 2018Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://www.sciencedirect.com/science/article/pii/S0165011418308194Versión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
For
a
continuous
function
f
on
a
Hausdorff
space
X
,
we
prove
that
[
̂
f(u)
]
α
=
f(u
α
)
for
each
u
∈
F
(X)
and
α
∈[
0
,
1
]
,
where
̂
f
is
the
Zadeh’s
extension
of
f
. ... [+]
For
a
continuous
function
f
on
a
Hausdorff
space
X
,
we
prove
that
[
̂
f(u)
]
α
=
f(u
α
)
for
each
u
∈
F
(X)
and
α
∈[
0
,
1
]
,
where
̂
f
is
the
Zadeh’s
extension
of
f
.
By
means
of
this
result,
some
results
on
(locally)
compact
spaces
and
the
Zadeh’s
extension
are
generalized.
Given
a
metric
space
(X,
d)
,
we
introduce
Skorokhod’s
metric
d
0
on
the
set
F
(X)
of
the
family
of
all
upper
semicontinuous
fuzzy
sets
u
:
X
→[
0
,
1
]
with
compact
support
and
such
that
u
−
1
(
1
)
is
non-empty.
We
show
that
if
f
:
(X,
d)
→
(X,
d)
is
a
continuous
function,
then
its
Zadeh’s
extension
̂
f
to
(
F
(X),
d
0
)
is
also
continuous
and
that
(X,
d)
is
separable
if
and
only
if
(
F
(X),
d
0
)
is
separable.
We
also
present
a
fuzzy
version
of
the
so-called
Hutchinson
operator,
a
valuable
tool
in
fractal
theory. [-]
Publicado en
Fuzzy Sets and Systems, online 29 October 2018Derechos de acceso
http://rightsstatements.org/vocab/CNE/1.0/
info:eu-repo/semantics/restrictedAccess
info:eu-repo/semantics/restrictedAccess
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