temperture is 37
o
C. The lowest temperature occurs on July-August, while the highest temperature occurs on October-November.
The average rainfall of the area is 170 mm with 82.8 rainy days. Wet season occurs between November to April, while dry season between May to
October. In the wet and dry seasons the relative humidity is around 76.4 – 78.4 and 73.6 – 78.8 respectively.
3.1.4 Demography
Demography is an important aspect on development planning. The demography of the study area is shown in Table 3.1 which is based on number
and composition of population, distribution and sex. Table 3.1 Demography of study area Source: Bureau of Statistical Centre, 2006
District Area
Ha Number
of Village
Population Male Female Head of
Household KK
Porong 2,982 19 64,019 34,690
29,329 21,670 Jabon 8,100 15 43,945 23,670
20,275 11,557 Tanggulangin
3,229 19 90,684 35,501
55,183 24,162
3.2 Required Tools
This research uses some supporting hardware and software. The hardware used is a unit of personal computer with Pentium IV processor, 512 MB RAM and
80 GB hard disk. Some supporting software are used to accomplish this research as listed in Table 3.2
31
Table 3.2 Software component
No. Software Function
1 Map Info 7.0
For spatial data process 2
Arc View 3.3 For spatial data process and analysis
3 ER Mapper 6.4
For image georeference 4
Ms. Excel 2003 For tabular and Fuzzy AHP process
5 Ms. Word 2003
For report writing
3.3 Framework of Vulnerability Analysis
The decision analysis of vulnerability for mud volcano adopts elements from the techniques of multi-criteria evaluation Malczewski 1999 with required
modifications. Proposed procedure was conducted in this research as shown in Figure 3.2.
32
Figure 3.2 Flow of the research process
3.3.1 Identification of Evaluation Criteria
The set of evaluation criteria is problem specific depending on the particular system being analyzed. The criteria selected should reflect all relevant
condition to the decision problem and must contribute toward achieving the objectives. There is no universal technique available for determining a set of
criteria. Likewise, a set of criteria is good if it is: 1 complete i.e. covers all aspects of a decision problem; 2 operational i.e. is meaningful to a decision
33
situation; 3 decomposable i.e. is amenable to partitioning into subsets of criteria, which may be necessary to facilitate a hierarchical approach to decision
analysis; 4 non-redundant i.e. avoids the double-counting of decision consequences; and 5 minimal i.e. has the property of the smallest complete set
of criteria characterizing the consequences of a decision. Developing criteria could be done through literature studies, analytical studies and survey of opinions.
This research used literature study and survey of opinion in form of interview and discussion to develop evaluation criteria. Literature study was done
to understand the relevant topics of mud hazard in Sidoarjo. Sources of the study include journal papers about impacts of hazard in Sidoarjo, monitoring reports of
Lapindo hazard by BPLS, and internet sources of official or reliable institutions. The interview and discussion with experts were used to facilitate
comparability and processing of results of literature study. Both interviews and discussions were done by face-to-face approach with some experts from various
discipline area i.e. BPLS, Centre of Environmental Geology and disaster researchers. Interview is used to gain an understanding of the underlying reasons
and motivations for people’s attitudes, preferences or behavior. People or a group of experts who will be affected by decision was asked to identify the criteria that
should be included in a decision analysis. In general an interactive, step-by-step, staged interview approach is followed: a first round with a few, general questions
and a subsequent round for more detailed specific questions.
34
3.3.2 Hierarchical Structure of The Criteria
The relationship between the objectives and attributes has a hierarchical structure in MCDA Malczewiski, 1999. At the highest level the objectives can
be distinguished, while at the lower levels the attributes can be decomposed.
3.4 Data Preparation
3.4.1 Data Collection
The main activity of the data collection is to extract list of data according to need analysis and expert knowledge to support evaluation criteria. The data is
extracted from the discussion with experts from BPLS and Centre of Environmental Geology, Bandung.
Data collected consists of secondary data including spatial data and non spatial data derived from supporting literatures, field survey of previous
researches and related maps of the region. To obtain the expert judgment regarding the scoring of the criteria, structured questionnaire and interview were
used. The spatial data of study area used for supporting the research include land
use type, RBI Rupa Bumi Indonesia – Indonesian Topography and evaluation criteria maps. Topography map RBI map with the scale of 1:25000 is acquired
from National Survey and Mapping Agency Bakosurtanal. Hazard criteria maps are obtained from BPLS and Centre of Environmental Geology Bandung.
Thematic map and hazard criteria map layers will be used and processed in the GIS analysis.
35
3.4.2 Generating Criterion Map
Having established a set of criteria for evaluating alternative decision, each criterion should be represented as a map layer in the GIS database. The criterion
map represents the spatial distribution of an attribute that measure the degree to which its associated objectives are achieved.
The main purpose of generating criterion map is to create hazard criterion map appropriate to vulnerability input map. This procedure for generating
criterion maps is based on GIS functions, which include geographical data input; data storage and management; data manipulation and analysis Malczewski,
1999.
3.5 Multi-criteria Evaluation
This research uses AHP Normal Pairwise Comparison Matrix to standardize the criteria and Fuzzy AHP to describe multi-criteria evaluation.
3.5.1 Normal Pairwise Comparison Matrices
The input of fuzzy AHP is crisp Pairwise Comparison Matrix PCM. This matrix shows the rate of relative preference for two criteria with the value from 1
to 9 Table 3.3.
36
Table 3.3 Scale of Relative Importance Source: Saaty, 1980
Intensity of relative
importance Definition Explanation
1 Equal importance
Two activities contribute equally to the objective
3 Moderate importance of one over another
Experience and judgment slightly favor one activity over
another
5 Essential or strong importance
Experience and judgment strongly favor one activity
over another
7 Demonstrated importance
An activity is strongly favored and its dominance is
demonstrated in practice
9 Extreme importance
The evidence favoring one activity over another is of the
highest possible order of affirmation
2, 4, 6, 8 Intermediate values between the two
adjacent judgments When compromise is needed
Reciprocals of above non-zero
numbers If an activity has one of the above numbers
e.g. 3 compared with a second activity, then the second activity has the reciprocal
value i.e., 13 when compared to the first
Multi-criteria decision analysis requires the values of the various criteria where the measurement of the values depends on the subjectivity of the personal
judgement of decision makers or experts. The evaluation criteria need to be standardized into common scale because they are represented by different
measurement scales. The value from PCM can be used for the purpose of rating or standardizing Malczewski, 2003. Criteria standardization is normally done on 0
to 1 scale, or 0-10 or 0-100, etc. The criteria at the lowest level that have different suitability classes are standardized using the maximum Eigenvectors approach on
0 to 1 scale. In mud volcano vulnerability, a map represents each evaluation with
values such as Z1, Z2, Z3 and Z4 indicating the degree of vulnerability with
37
respect to a criterion which is based on the requirements. These classes will be rated based on the importance of vulnerability class with respect to a particular
criterion.
3.5.2 Fuzzy AHP
The steps of Fuzzy AHP for vulnerability analysis are shown in Figure 3.3. PCM from AHP is fuzzified to get the Fuzzy PCM. Fuzzy extent analysis is then
applied to calculate performance ratings and criteria weights for the Fuzzy PCM. Performance ratings are then multiplied by criteria weights according to hierarchy.
The result is a range of values over which any value can be considered as performance value. Decision makers are then requested to give their confidence
level regarding their judgment. The confidence level will be taken as α-cut value,
which will have a range of value between 0 – 1. In addition, decision makers attitude play a role in deciding the performance value. Up to this point, the
performance is still in interval values. Pessimistic, optimistic or middle decision maker attitude will determine which value will be chosen, either the lowest value,
highest value or middle value respectively. Pessimistic decision maker attitude is expressed as Optimism Index
λ which value is between 0 - 1. Using the optimism index, the fuzzy range is once again converted into a crisp range.
38
Figu steps fo
erabilit
3.5.3 uzzy AHP Ap
n Vulnerabil nalysis
the fuzzy AHP approach, triangular fuzzy numbers were used for the fuzzification of the crisp PCM. The crisp PCM is fuzzified using the triangular
fuzzy number f = l, m, u. The l lower bound and u upper bound represents the vague range that might exist in the preferences expressed by the decision
maker or experts. Conversion from crisp re 3.3 Fuzzy AHP
r vuln y Analysis
F proach i
ity A
In
to Fuzzy PCM is shown in Table 3.4.
39
Table 3.4 Conversion of crisp PCM to fuzzy PCM Source: Deng, 1999 in Kuswandari, 2004 and Prakash, 2003
Crisp PCM value
Fuzzy PCM value Crisp PCM
value Fuzzy PCM value
1 1, 1, 1 if diagonal
1, 1,3 otherwise 11
11, 11, 11 if diagonal 13, 11, 11 otherwise
2 1, 2, 4
12 14, 12, 11
3 1, 3, 5
13 15, 13, 11
5 3, 5, 7
15 17, 15, 13
7 5, 7, 9
17 19, 17, 15
9 7, 9, 11
19 111, 19, 17
Given a crisp PCM A, having the values ranging from 19 to 9 ⎟
⎞ ⎜
⎜ ⎜
⎛ =
n
a a
a a
A ...
... ...
21 1
12 11
⎟ ⎟
⎜ ⎜
.. ...
... ..
. ⎟
⎟ ⎟
⎠ ⎜
⎝
n
a a
a a
a
... ...
. ..
.. ...
... ...
... ...
2 22
3.1
parison atrix
mn m
m 2
1
where
11
a to
mn
a are the score values obtained from AHP pairwise com
m The fuzzy PCM
.
A
will be as follows,
⎟ ⎟
.. ...
... ...
... ⎟
⎟
⎠ ⎜
⎜ ⎜
⎜ ⎜
⎜
⎝ ⎛
= ...
... ...
...
l
a a
a a
a a
a a
a a
a a
a a
a a
a a
a 3.2
where pairwise comparison matrix which are fuzzified using the rule from Table 3.4.
Using fuzzy PCM, fuzzy extent analysis then is applied to obtain the fuzzy performance matrix of each alternative with respect to all criteria. The fuzzy
performance X and fuz for vulnerability analysis are shown as
follows: ⎟
⎞ ...
...
1 1
1 12
12 12
11 11
11 u
n m
n l
n u
m l
u m
l
a a
a a
a a
a a
⎟ ..
... ...
... ...
2 2
2 22
22 22
21 21
21 u
n m
n l
n u
m l
u m
A
2 2
2 1
1 1
u mn
m mn
l mn
u m
m m
l m
u m
m m
l m
a
11l
a
11m
a
11u
to a
mnl
a
mnm
a
mnu
are the score values obtained from AHP
zy weights W
40
∑ ∑∑
−
⎤ ⎡
n m
n 1
−
⎤ ⎡
k l
k 1
= j
i 1
= =
⎥ ⎦
⎢ ⎣
⊗ =
i j
j i
j i
a a
x
1 1
= =
⎥ ⎦
⎢ ⎣
⊗ =
j i
j j
i j
i j
b b
w
1 1
1
3.3
here f vulnerable class i
uzzy PCM
∑ ∑∑
=
w x
i
= fuzzy performance value o w
j
= fuzzy weight value of criteria i a
i
= vulnerable level of class i to class j in the f
A
b
i
= importance of criteria i to criteria j in the fuzzy PCM
B
i = 1, 2, 3,…, n; number of rowscolumns vulnerable class in the PCM
j = 1, 2, 3,…,k; number of rowscolumns criteria in the PCM
The result in fuzzy performance matrix X and fuzzy weights W will be like shown below,
⎞ ⎜
⎜ ⎜
⎛
2 2
2 1
1 1
u m
l u
m l
x x
x x
x x
3.4
⎟
⎜ ⎜
= ...
... ...
W 3.5
⎟ ⎠
⎜ ⎝
u i
m i
l i
x x
x
⎟ ⎟
⎟ ⎟
⎠ ⎞
⎜ ⎜
⎜ ⎜
⎝ ⎛
... ...
...
2 2
2 1
1 1
ju jm
jl u
m l
u m
l
w w
w w
w w
w w
w
where X
⎟ ⎟
⎜ ⎜
= ...
... ...
... ...
...
j
X ⎟
⎟ ⎟
⎟
j
= performance matrix of vulnerable class for criteria j W
= weight matrix of criteria i = 1, 2, 3, …, n; number of vulnerable class
j = 1, 2, 3, …, k; number of criteria
41
A fuzzy weighted performance matrix P can thus be obtained by multiplying the weight from the weight vector with the decision matrix over the
hierarchy.
⎜ ⎜
= ⎟
⎟ ⎜
⎜ =
= ..
... ...
... ...
...
2 2
2 2
2 2
m l
u m
l
w w
w w
X P
⎟ ⎟
⎠ ⎜
⎜ ⎝
⎟ ⎟
⎠ ⎜
⎜ ⎝
... ...
... ...
... ...
u n
m n
l n
u i
m i
l i
where P ⎟
⎟ ⎟
⎟ ⎞
⎜ ⎛
⎟ ⎞
⎜ ⎛
1 1
1 1
1 1
u m
l u
m l
p p
p x
x x
⎜ ⎟
⎜ .
u ju
jm jl
j j
j
p p
p p
p p
x x
x x
x x
3.6
α
preference or judgment and the result will be a single value having the membership 1 in the fuzzy performance set. It means no further step is required.
If α-cut is less than 1 then there is degree of vagueness from the expert or decision
maker related to the preference or judgment. On the other hand if the α-cut = 0, it
expresses the highest vagueness of the expert or decision maker regarding the preference and judgment; therefore the possible performance will be whole
n 1 will need further evaluat
j
= fuzzy weighted performance matrix of criteria j The next step is to calculate the interval performance matrix using the -cut
over the result above. Alpha-cut is known for enabling to include the decision maker or expert confidence about the preference or judgment that has been made.
Applying the α-cut will result to the interval performances. The α-cut value
ranges from 0 to 1. If the α-cut = 1 then the expert is very sure about the
support of the fuzzy performance. Any value of α less tha
ion to get the crisp performance.
42
⎟ ⎟
⎟ ⎟
⎜ ⎝
] ,
[ ...
] ,
[
2 2
ir il
r l
p p
p p
p p
⎟ ⎠
⎜ ⎜
⎜ ⎜
⎜ ⎛
= ]
, [
3 3
r l
j
P
α
3.7
where l and r represent the left and right value of the interval set. Th
ptimum index. Lambda function enables to include the decision maker or expert attitude
about judgment that has been made. The λ value ranges from 0 to 1. If the λ= 1
then the expert is very sure about the judgment. On the other hand if the λ = 0, it
expresses the lowest attitude of the expert or decision maker regarding the judgment. In the current studies of hazard vulnerability, this function will serve to
represent boundaries of vulnerability classes. Optimism index λ is applied over
the interval performance set that will result in the performance matrix C.
α-cut analysis P
α
il
= the left most value obtained from α-cut analysis.
The equation will give the crisp performance matrix,
3.9
where = crisp performance matrix of criteria i
c
1
…c
i
= crisp performance value of vulnerable class i ⎟
⎞ ]
, [
1 1
r l
p p
e crisp performance matrix is obtained by applying λ the o
1
l j
r j
j
P P
C
α
λ λ
∗ −
+ ∗
=
, with λ = [0, 1]
3.8 where P
α α
λ
α
ir
= the right most value obtained from
⎟⎟ ⎟
⎟ ⎟
⎠ ⎞
⎜⎜ ⎜
⎜ ⎜
⎝ ⎛
=
i j
c c
c C
...
2 1
λ α
λ α
Cj
43
3.6 Generating Vulnerability Map
Once weighted performance of each criterion have been converted into crisp performance value, Spatial Analysis over criteria layers can be performed
for Fuzzy AHP.
Figure 3.4 Aggregation of the ratings and weights over hierarchy
Figure 3.4 shows the steps of generating vulnerability map. Firstly, criteria layers are classified accordingly to the vulnerability class Z1 – Z4. The
next step is applying crisp performance value that is acquired from fuzzy AHP process to each criterion map to obtain weighted criteria layers. After that,
44
combines the weighted value of criterion map by summing up the crisp performance value of map layers. This will give the final result of vulnerability
ratings at the final level. The final vulnerability ratings are then classified into final vulnerability map. The classification will be based on the value for Z1 – Z4
acquired from performancesweights calculation.
Figure 3.5 The process to generate weighted criterion layer
erion map to acquire the weighted criterion layer
rangevalue is s bility class of
this range is identified from standard vulnerable class information. After that, choose the proper crisp performance of this class to result the weighted criterion
layer. This process is performed to all criteria layers. The procedure to apply crisp performance value to the crit
is shown in Figure 3.5. Firstly, the elected from criterion layer. Then, the proper vulnera
45
3.7 Sensitivity Analysis
