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Title
The 3rd ISPRS Workshop on Dynamic and Multi-Dimensional GIS & the 10th Annual Conference of CPGIS on Geoinformatics
Author
Chen, Jun

ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS", Bangkok, May 23-25, 2001
305
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