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[
μ
]
All this crisp partial orderings come from the fuzzy ordering given by
, and
which valued directed graph is
5
6
0.6
0.5
0.4
2
3
4
0.2
0.8
0.6
1
where some arrows are avoided because of the min-transitivity of
μ
. For instance,
the degree between 1 and 5, is
μ(
1
,
5
)
=
Max
1
min
(μ(
1
,
k
), μ(
k
,
5
))
=
max
(
min
(
0
.
8
,
0
.
6
),
k
6
min
(
0
.
2
,
0
.
5
))
=
0
.
6
,
and the strengh of the order between 1 and 6, is
μ(
1
,
6
)
=
Max
1
k
6
min
(μ(
1
,
k
), μ(
k
,
6
))
=
min
(
0
.
6
,
0
.
4
)
=
0
.
4
.
μ(
,
)
=
μ(
,
)
=
...
=
μ(
,
)
=
Of course,
1
1
2
2
6
6
1.
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