not impacted class an 1
a g
h r
F 4
sho e vuln
bilit ss
p e
en r
d ro
above at alpha 0.6 and lambda 0. d 1 are reco nized as hig
haza dous. igure
.12 ws th
era y cla es ma for s ttlem
t area esulte from the p cess
Figure 4.12 The vulnerability map at alpha 0.6 and lambda 0
4.7 Sensitivity Analysis
nalysis is used to enlighten the effect of uncertainty in expert knowle
confidence of expert pr
t e expert is
pha value 0.6 and 0.8 indicate that Sensitivity a
dge. Alpha-cut is known to include the decision maker or expert confidence about the preference or judgment that has been made. Applying alpha
values less than 1 result in the interval performances. This research used three different alpha values 0, 0.6 and 0.8 to address the
eference. An alpha value of 0 indicates highest vagueness and 1 indicates tha th
very sure about the preference. Al
73
t ci
iro is e
u e e
n d a
od an
p nfi
e l ve f e
ec y. n
alu at
h 1 w
further evaluation to get the crisp perf a
mbda f
erformance of Fuzzy AHP for mud volcano vulnerability at several lambda values is shown in Table 4.16.
he de sion env nment c rtain p to som
xtent a d esign tes the m erate
d o timism co denc
e l o
xpert resp tivel A y v
e of α th less
t an ill need
orm nce. In the last stage la
unction was applied to convert the range value of expert preference into crisp value. This current research applied three different lambda values 0, 0.5 and
1 to address the attitude of the expert about their preference or judgment. These lambda values were applied for each alpha value.
There are three scenarios of uncertainty related to the performing of three different alpha values. This scenarios show how the uncertainties involved in
vulnerability decision making process will influence the outcome of the process. The crisp p
Table 4.16 Crisp performance of criteria at several alpha and lambda values
Alpha cut 0.4 Alpha cut 0.6
Alpha cut 0.8 Criteria
Vulnerable Class
λ = 0 λ = 0.5
λ = 1 λ = 0
λ = 0.5 λ = 1
λ = 0 λ = 0.5
λ = 1
Z1 0.031 0.147 0.263
0.041 0.118 0.195 0.050 0.089 0.127
Z2 0.015 0.078 0.141
0.019 0.061 0.104 0.024 0.045 0.066
Z3 0.006 0.035 0.064
0.007 0.027 0.046 0.009 0.019 0.029
Subsidence 0.003 0.015 0.026
0.004 0.012 0.019 0.005 0.009 0.013
Z4 Z1
0.028 0.347 0.665 0.040 0.253 0.465
0.053 0.159 0.265 Z2
0.014 0.186 0.358 0.020 0.134 0.249
0.026 0.083 0.140 Z3
0.007 0.099 0.191 0.009 0.071 0.133
0.012 0.043 0.074 CH4
Z4 0.003 0.034 0.066
0.004 0.025 0.046 0.005 0.015 0.026
Z1 0.009 0.140 0.270
0.013 0.100 0.187 0.017 0.061 0.104
Z2 0.004 0.080 0.156
0.006 0.057 0.107 0.008 0.034 0.059
Z3 0.003 0.047 0.092
0.004 0.034 0.063 0.005 0.020 0.035
H2S Z4
0.001 0.024 0.047 0.002 0.017 0.033
0.003 0.010 0.018 Z1
0.003 0.039 0.076 0.004 0.028 0.052
0.005 0.017 0.029 Z2
0.002 0.027 0.052 0.002 0.019 0.036
0.003 0.011 0.020 Z3
0.001 0.017 0.033 0.001 0.012 0.023
0.002 0.007 0.012 CO2
Z4 0.001 0.009 0.017
0.001 0.006 0.011 0.001 0.004 0.006
74
Table 4.16 Crisp performance of criteria at several alpha and lambda values continued
Alpha cut 0.4 Alpha cut 0.6
Alpha cut 0.8 Criteria
Vulnerable Class
λ = 0 λ = 0.5
λ = 1 λ = 0
λ = 0.5 λ = 1
λ = 0 λ = 0.5
λ = 1
Z1 0.107 0.516 0.924
0.144 0.417 0.689 0.182 0.318 0.454
Z2 0.059 0.301 0.542
0.080 0.241 0.403 0.101 0.182 0.263
Z3 0.028 0.151 0.273
0.039 0.120 0.202 0.049 0.090 0.131
Water Quality
Z4 0.009 0.039 0.068
0.011 0.031 0.051 0.014 0.024 0.034
Z1 0.107 0.516 0.924
0.144 0.417 0.689 0.182 0.318 0.454
Z2 0.059 0.301 0.542
0.080 0.241 0.403 0.101 0.182 0.263
Z3 0.028 0.151 0.273
0.039 0.120 0.202 0.049 0.090 0.131
Flooded 034
Area Z4
0.009 0.039 0.068 0.011 0.031 0.051
0.014 0.024 0.
lue of the range. The variation of performance for each criterion under several classes at specific alpha
l n Table 4.16.
This will effect on final vulnerability class Z1 – Z4 that are classified a
. The three
os of effe s on the percenta
of vulne a as a
re t o
se al a ph
al sure the vagueness of expert about
th co
are ussed in deta
ws:
Scenario 1
vulnerable area for this alpha value is shown in Table 4.17. Applying different alpha values resulted dissimilar interval of
performance. The crisp performance values that represent attitude of expert about this range are chosen at maximum, medium and minimum va
va ue is shown i The consequence of applying several alpha and lambda value is the
difference performance for each criterion relative to vulnerability class Table 4.16.
b sed on these performance values and also on percentage of vulnerability area scenari
ct area and
ge rable are
sul f applying
ver l
a v ues to mea eir
nfidence disc
il as follo •
Scenario 1 uses alpha value 0.4 to represent confidence of expert preference or judgment. The interval of performance for each criterion of this
alpha value is the largest among the three alpha values Table 4.16. The
75
Table 4.17 Vulnerability area under different classes and lambda at alpha 0.4
Lambd a 0
Lambda 0.5 Lambda 1
Class Area m
2
Area Class Area
m
2
Area Class Area
m
2
Area
Z3 2043708.869 51.4 Z3 1470779.085 37.0 Z3 1536283.470 38.6 Z1 1473395.692 37.0 Z2 1437688.215 36.1 Z2 1450275.363 36.5
Z2 326933.398 8.2 Z4 1069449.409 26.9 Z4 991256.739 24.9
Z4 133437.632 3.4
cted class Z4.
Area with low hazardous class consist of 38.6 of the total area, followed by moderate hazardous covering 36.5 and not impacted
cla er
this lambda value. Lambda value can be used to measure the vagueness of the expert
confidence. The lowest attitude lambda 0 shows the highest sensitivity of vulnerability class for alpha 0.4. The class Z2, Z3 and Z4 are no more sensitive
for λ ≥ 0.5. The expert knowledge is most sensitive in class Z1.
The vulnerability class map for alpha 0.4 with several lambda values is displayed in Figure 4.13.
At minimum value of interval performance, the low hazardous class Z3 covers 51.4 of the available settlement area, 37 of the area is categorized as
high hazardous class Z1, 8.2 of the area as moderate hazardous Z2 and 3.4 of the area recognized as not impa
At medium value of interval performance, class Z3 decreases to 37 of the area although it still covers the largest area, class Z2 covers 36.1 of the area,
class Z4 covers 26.9 of the area, while class Z1 is restricted, it does not occupy any area.
At maximum value of interval performance, the classes perform the same order as under
λ = 0.5.
ss with 24.9 of the total area. The high hazardous area is not available und
76
Figure 4.13 Vulnerability class map at alpha 0.4 under several lambda value
Figure 4.13 shows t t
hi vity
cur at bda value 0 wh
lass Z1 consists of up to 37 of the total areas, but it does not found anymore at λ ≥ 0.5. This sensitivity also occurs in class Z2, Z
Scenario 2
Scenario 2 uses alpha value 0.6 to represent confidence of expert preference or judgment. The vulnerable area for this alpha value is shown in Table
4.18. Table 4.18 Vulnerability area under different classes and lambda at alpha 0.6
Lambda 0 Lambda 0.5
Lambda 1
ha the gh sensiti
oc s lam
ere c
3 and Z4.
•
Class Area m
2
Area Class Area
m
2
Area Class Area
m
2
Area
Z3 49.6
Z3 50.2
Z3 39.7
1974506.366 1997533.071
1579999.098 Z2
994770.507 25.0
Z2 1424091.291 35.8 Z2 1450275.363
36.5 Z4
14.4 Z4
13.6 574475.641
541580.564 Z4 947390.068
23.8 Z1
434013.128 10.9
Z1 14560.717 0.4
s class covering 49.6 of the total area. The moderate hazardous class covers 25 of area. The not
Using minimum value of interval performance, all of vulnerable classes are identified and the most areas belong to low hazardou
77
impacte
al performance, class Z3 still has the largest area covering 50.2 of the total area and Z2 covers 35.8 of the area. Class Z4
occupies 13.6 and class Z1 is restricted to only 0.4 of the area. Using maximum value of interval performance, the moderate hazardous
class squeezes to 39.7 of the total area, followed by class Z2 covering 36.5 of the area, while Z4 extends to 23.8 of the area. The high hazardous class is
uncovered for this lambda value. of
perform d class and high hazardous class cover 14.4 and 10.9 respectively of
the total area. Using medium value of interv
The application of 60 expert confidence can shorter the interval ance. Classes Z3 and Z4 are no more sensitive to
λ ≤ 0.5. Class Z2 is no more sensitive to
λ ≥ 0.5. Class Z1 is sensitive at the lowest attitude, but no more sensitive to
λ ≥ 0.5. The vulnerability class map for alpha 0.6 with several lambda values is
displayed in Figure 4.14.
Figu
Figure 4.14 shows the effect of 60 confidence level of expert about their preference or judgment to vulnerability class. The use of this moderate alpha
re 4.14 Vulnerability class map at alpha 0.6 under several lambda value
78
value shows sensitivity of class Z1 for λ = 0, class Z2 for λ ≤ 0.5, class Z3 and Z4
for λ ≥ 0.5.
• Scenario 3
Scenario 3 uses alpha v repre
confidence of expert preference or judgment
e inte rmance for each criterion at this
alpha is the shortest among the three alpha values Table 4.16. The vulnerable area fo
alue 0.8 to sent
. Th rval of perfo
r this alpha value is shown in Table 4.19. Table 4.19 Vulnerability area under different classes and lambda at alpha 0.8
Lambda 0 Lambda 0.5
Lambda 1 Class Area
m Area
Class Area m
Area Class Area
m Area
2 2
2
Z3 1988286.333
50.0 Z3 1990431.245
50.0 Z3 1997533.071
50.2 Z2
25.0 Z2
32.7 Z2
35.8 995466.472
1301317.921 1424091.291
Z4 559999.709
14.1 Z4 542883.390
13.6 Z4 541580.564
13.6 Z1
10.9 Z1
3.6 Z1
0.4 434013.128
143133.087 14560.717
At minimum attitude of expert, the low hazardous class covers 50 of the available area, 25 of area belongs to moderate hazardous class, 14.1 of area is
categor ed as not impacted class and 10.9 area is recognized as high hazardous class.
nd Z2 is restricted only to 32 ass Z4 covers 13.6 area and
class Z1 only 3.6 of the area. iz
At medium attitude of expert, class Z3 dominate with 50 of the total area .7 of the area. Cl
a
At maximum attitude of expert, 50.2 of the area belongs to moderate hazardous class, followed by class Z2 that covers 35.8 of the area and Z4 with
13.6. The high hazardous area tightens to 0.4 of area.
79
The application of 80 expert confidence shows that class Z3 and Z4 are not sensitive for all interval value. The class Z2 is no more sensitive to
λ ≥ 0.5. The sensitivity of class Z1 also decreases for this alpha.
The vulnerability class map for alpha 0.8 with several lambda values is displayed in Figure 4.15. This figure shows that class Z3 and Z4 are not sensitive
by using optimism confidence level.
Figure 4.15 Vulnerability class map at alpha 0.8 under several lambda value
These three mentioned above scenarios illustrate that the alpha cut shows the interval performance according to the vagueness of expert confidence, while
the lambda can be used to measure the vagueness of expert knowledge at specific attitude value between these intervals. Performing three scenarios show that the
highest sensitivity can be observed at alpha 0.4 and lambda 0. The class Z3 and Z4 are no more sensitive at optimum alpha value, while class Z2 is not more
sensitive for λ ≥ 0.5 at all alpha value. The choice of alpha 0.6 and 0.8 at λ ≤ 0.5
illustrate the vulnerability area that is nearly same, especially for lambda 0.
80
4.8 C
