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In-Depth Information
∈
(
,
)
μ
R
(
,
)
=
with
k
0
1
a parameter chosen at each particular case, it is
0
0
0,
μ
R
(
,
)
=
μ
R
(
,
)
=
μ
R
(
,
)
=
(
,
)
=
μ
R
(
/
,
)
=
μ
R
(
,
/
)
=
1
1
0,
0
1
1
0
max
0
k
k
,
1
2
1
1
1
2
max
(
0
,
k
/
2
)
=
k
/
2, etc., with the graphic,
z
k
y
k
k
x
When the sets
X
1
,...,
X
n
are finite,
μ
R
is reduced to a matrix. For example if
X
1
={
x
1
,...,
x
p
}
, and
X
2
={
y
1
,...,
y
q
}
, then
μ
R
(
x
i
,
y
j
)
=
r
ij
,1
i
n
,1
j
m
,or,
μ
R
=
r
11
/(
x
1
,
y
1
)
+···+
r
nm
/(
x
n
,
y
m
)
,
that gives the
n
×
m
matrix
⊛
⊝
⊞
⊠
.
r
11
r
12
...
r
1
m
...
r
21
r
22
r
2
m
[
R
]=
.
.
.
r
n
1
r
n
2
...
r
nm
In the finite case there is again another representation of a fuzzy relation by means
of a directed graph. For example, if
X
1
={
x
1
,
x
2
}
and
X
2
={
y
1
,
y
2
,
y
3
}
, the fuzzy
0
, corresponds to the directed graph
.
50
.
71
relation
[
R
]=
0
.
800
.
8
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