Information Technology Reference
In-Depth Information
Ta b l e 1 .
Parameters and shapes of the example
T
ij
UMF LMF
L
ij
(
x
)
R
ij
(
x
)
T
12
= (1,1.5,1,1) (1, 1.5, 0.8, 0.8)
L
12
(
x
)=max(1
− x
2
,
0)
R
12
(
x
)=max(0
,
1
− x
)
T
13
= (2,3,0.3,2.4)
L
13
(
x
)=exp
−x
(2,3,0,2)
R
13
(
x
)=max(0
,
1
− x
)
T
24
= (0,0,0,0)
(0,0,0,0)
L
24
(
x
)=max(0
,
1
− x
)
R
24
(
x
)=max(0
,
1
− x
)
T
25
= (2,3,1.4,2.3)
L
25
(
x
)=max(0
,
1
− x
4
)
R
25
(
x
)=exp
−x
(2,3,1,2)
T
34
= (0,0,0,0)
L
34
(
x
)=max(0
,
1
− x
)
R
34
(
x
)=max(1
− x
2
,
0)
(0,0,0,0)
T
36
= (6,7,0.5,2.5)
L
36
(
x
)=exp
−x
2
R
36
(
x
)=max(1
− x
2
,
0)
(6,7,0,2)
T
46
= (5,5,1.1,1.2)
L
46
(
x
)=max(0
,
1
− x
)
R
46
(
x
)=max(0
,
1
− x
4
)
(5,5,1,1)
T
47
= (9,9,1.4,1.6)
L
47
(
x
)=max(0
,
1
− x
4
)
R
47
(
x
)=exp
−x
(9,9,1,1)
T
59
= (8,9,2.3,4.7)
L
59
(
x
)=max(0
,
1
− x
4
)
R
59
(
x
)=max(1
− x
2
,
0)
(8,9,2,4)
T
68
= (4,4,2.6,2.8)
L
68
(
x
)=max(1
− x
2
,
0)
R
68
(
x
)=max(0
,
1
− x
4
)
(4,4,2,2)
T
78
= (3,4,2.5,0.3)
L
78
(
x
)=max(0
,
1
− x
)
R
78
(
x
)=max(0
,
1
− x
4
)
(3,4,2,0)
T
89
= (6,9,2.2,3.7)
R
89
(
x
)=exp
−x
2
L
89
(
x
)=max(1
− x
2
,
0)
(6,9,2,3)
1
0.8
FOU of
D
J
d
0.6
0.4
0.2
0
10
15
20
25
30
35
40
45
50
55
60
d
D
Fuzzy set of optimal solutions
Fig. 3.
Fuzzy set
D
composed from optimal project times
4.2
Analysis of Results
The shape of the left function for the optimal solution shows the same critical path (1-
3-4-7-8-9) for several
ʱ
-cuts, the minimal optimistic time for the external left function
and the internal left function is approximately 12 and 15 respectively. Table 2 shows
that the project has three possible CPs (1-2-4-7-8-9), (1-3-4-7-8-9), (1-3-6-8-9) which
can occur anytime in the project, so the analyst should pay attention to CPs and their
activities when performing the project to identify when a CP will switch to another one.
The internal right bound presents a different CP (1-3-6-8-9) from 0.1 to 0.8
ʱ
-cut
and its maximal pessimistic time is approximately 49, the external right bound presents
a similar behavior changing the CP from 0.2 to 0.9
ʱ
-cut and its maximal pessimistic
time is approximately 59.
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