ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS", Bangkok, May 23-25, 2001 
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permit at imprecision and partial occurrence, which is not 
compatible with actual decision making process. Frequently, 
decision making in spatial assessment involves uncertainty due 
to incompleteness of the data acquired and the variety of 
evaluation tools used to gather data. In addition, numerical 
measurements in compactness measurements give uncertain 
and vague value for accurate assessment of district 
compactness and continuity. Altman’s axiomatic assessment on 
most of the compactness measurements show that existing 
compactness measurement do not accurately assess compact 
district shape. 
non-spatial data, their relationship and dependency 
The domain and task of the proposed model is at enhancing the 
decision support system in maintaining the compactness and 
continuity of the shape based redistricting to produce the optimal 
compact district plan. Fuzzy Multi Criteria Decision Making 
(FMCDM) will be used to enhance this component of the model. 
GIS analysis tools is used as an important supportive tools for 
this model because of its capability to due with relationships of 
spatial and non-spatial data. Besides, it also provides numerous 
ready-to-use functions for a shape based redistricting. 
There is a lot of redistricting techniques but still does not give an 
ideal district plan in term of geographical aspect. Redistricting 
cannot run away from compactness and continuity. Many 
redistricting problems suffered for the spatial context problem. 
However, there is no incorporation of compactness 
measurement to redistricting techniques to get optimal compact 
district. The complexity of the data structures and the data 
volumes are the also common problems to be solved in 
redistricting arena. Due to the complexity of the data structure, 
there is an insufficiency in collecting relevant data. For instance, 
in the political redistricting, there is no single source contains all 
geographical and population data for the United States 
congressional district over the entire period from 1789 through 
1912 [1]. The complexity of data structures needs certain kind of 
solution that is able to assign and cope with different kind of 
behavior like the spatial and non-spatial behavior, consider their 
relationships and dependencies in order to ease the 
manipulation of each part. For instances, in order to consider the 
non-spatial behavior in redistricting, there is a necessity to find 
solution where it is possible to store, manipulate, visualize, and 
relate data especially for other spatial behavior. It is certainly 
that redistricting will not be done by only single type of data. 
Therefore, the relationship between data and behavior plays an 
important role. 
3. COMPACTNESS MEASUREMENT INDEXING USING 
FUZZY MULTICRITERIA DECISION MAKING 
3.1 The Design and Model 
The following subsections describe the proposed design model 
for the shape based redistricting based on the requirement 
mentioned as shown in Figure 1.0. The components of the 
proposed integrated model are Application Independent Data 
Store (AID), Application Dependent Data Store (ADD), Shape 
Optimal Rules (SOR), Data Preparation Module (DPM), Fuzzy 
Multi Criteria Decisions Making (FMCDM), Combine Optimal 
District Module (COD) and stages of decision making. 
AID 
DPM 
ADD 
SOR 
FMCDM 
». s, 
& 
». s. 
COD 
AID -Application Independent Data. Store 
ADD - Application Dependent Data Stcee 
SOR— Shape Optimal Rules 
DPM - Data Preparation Module 
FMCDM - Rizay Multi Catena Decision Making Modules 
COD - Cantane Optimal District Module 
Si, Si, Si-Stages of decision malt ing 
Figure 1.0: Integrated Compactness Measurement Using Fuzz 
Multiple Criteria Decision Making 
The proposed system aims to get optimum or compact district, 
which defined as in this research is as regular and contiguous as 
possible and at the same time to use the natural boundaries 
where possible in the district line. The main significance is to 
ease the control of a space. For example, with regular and 
continuous districts, governors face less difficulty in ruling a 
district or even country in political redistricting. 
In order to solve the problems mentioned, the system design 
must be able to fulfill the requirements as stated below: 
• To produce better or enhanced shape assessment index 
which is more descriptive and able to incorporate with 
natural feelings of district planners or decision makers. 
Natural feelings here may include their confidence and 
their attitude to risk. 
• To cope with fuzziness in the shape assessment index. 
• To integrate multiple compactness measurement method in 
order to gather the strengths of particular method and at 
the same time to reduce or minimize its weaknesses or 
lacks. 
• To incorporate the new index into redistricting process or 
algorithm to generate an optimal compact district. 
• To work and perform in an environment (software or 
hardware interface) that is able to manage the spatial and 
Data Preparation Module (DPM) will used to prepare data in 
triangulated irregular network format to ensure the model can 
work with appropriate datasets. A triangulated irregular network 
is made up of arcs, which define the boundary, and a label point, 
which links the polygon feature to an attribute record. As the 
mother of all polygon partitioning problems is triangulation, the 
interior of all kind of polygons can be completely partitioned into 
triangles [6]. 
3.2 Applying Fuzzy Set Theory for Compactness 
Measurement In the SOR 
Shape Optimal Rules play an important role for the standard of 
the optimality of district shape. This component is related to the 
application independent data because the focus of the research 
is on the geographical aspect. 
Two compactness measurement methods are selected to gather 
the district boundary complexity and district compactness, which 
is Euclidean measure and non-Euclidean measure. More than 
one measurements are used in this research aims to combine 
the strengths of each measurement to the district compactness 
and to reduce their weaknesses by the weighing vector which 
will be incorporated into the enhanced index. The compactness 
measurement index for both of the methods give a gray area 
(undecided) for district planners or decision makers on the 
district shape assessment. Therefore, fuzzy set theory as will be