ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001
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INTEGRATION OF COMPACTNESS MEASUREMENT METHODS USING FUZZY MULTICRITERIA
DECISION MAKING : A NEW APPROACH FOR COMPACTNESS MEASUREMENT IN SHAPE BASED
REDISTRICTING ALGORITHM
Yinchai WANG
Faculty of Information Technology, Universiti Malaysia Sarawak,
94300 Kota Samarahan, Sarawak, MALAYSIA
Tel:+60-82-671000 ex377, Fax:+60-82-672301, E-mail:ycwang@fit.unimas.my
Chinwei BONG
Faculty of Information Technology, Universiti Malaysia Sarawak,
94300 Kota Samarahan, Sarawak, MALAYSIA
ABSTRACT
Thousand of district plans are generated from the redistricting processes but most of the processes are unable to determine the best
alternative. This paper will discuss the limitation of existing redistricting algorithms especially on redistricting applications based on the
geographical compactness that seems to have great limitation because it causes the redistricting processes more complex and
intractable. Spatial complexity for redistricting like topography factors causes inflexibility on conventional computer and also difficulties
was found especially in spatial aspect like geographical size, district shape and boundary lines which bring to the issues of
compactness and continuity. This paper presented a new approach for compactness measurement in a shape based redistricting
planning by using fuzzy multiple criteria decision-making to enhance the redistricting process especially on district compactness and
continuity. The design and development process of the proposed approach will also highlighted in this paper including generation of
compactness index based on the synthesis of the concepts of fuzzy set theory, AFIP,a-cuts concept and index of optimism of district
planners to estimate the degrees of satisfaction of the judgements on a district plan. The performances of the proposed new approach
was tested on a forest blocking prototype to demonstrate its applicability in redistricting applications with respect to their redistricting
goals and criteria. The results shown the proposed method is more flexible, simple and comprehensive with easy computation and
efficiency which facilitates its uses in compactness measurement in redistricting applications.
1. INTRODUCTION
According to Altman [2], Ronald Reagan was not the only recent
academic to state that computer could remove the controversy
from redistricting and it can find the “optimal” redistricting plan
by given any set of values that can be specified. In order to draw
a fair and unbiased district, the methods and algorithms
concerned are playing an important role and none of the
methods is specifically being determined as a standard.
Although redistricting is an optimization problem, different
solutions on integer programming or linear programming are still
did not offer the best solution. The geographical features play an
important role and the measures of geographical shape will be
an enormous endeavor in enhancing the redistricting result from
the application dependent factor. However, traditional
redistricting measures on spatial features are unsatisfactory to
produce the optimal result in terms of their compactness and
continuity. Thus, few efforts to create an optimum district
boundary has been proposed and one of the ideas is to use
fractal dimension to measure the spatial features in the
redistricting application.
Previous efforts on redistricting can be analyzed in two
perspectives of a district plan. Hence, district plan is defined as
the output of the redistricting process. Firstly, it is about the
standards to evaluate the district plan. These standards refer to
the compactness measurement techniques. Second, it is on the
redistricting methods, techniques or algorithms in creating
district plan. The existing standard to evaluate and assess the
district plan is use compactness measurements. These
compactness measurements encompass continuity and
therefore it means that the maximally compact plan would not
measurably and avoidably noncontiguous [2]. Therefore,
although the evaluation tools are called compactness
measurements, they assess not only on the compactness but
also on the continuity of the districts in the plan.
The primary concern on the proposed redistricting system is on
the shape regularity and the continuity of the district. The main
objective of the proposed system is to improve the compactness
measurement index through enhancement of the decision
making process through the used of dynamic programming
technique. The method used to redraw the redistricting boundary
in this research is the FMCDM methods as to draw optimal
district shape or to get optimal compact district plan. Therefore,
the compactness measurement technique will be used as
criteria in measuring the shape compactness or regularity and
continuity. Although there are many compactness measurement
methods, FMCDM may enable more than two methods being
used in the integrated model. Besides, the advanced OR
technique with the fuzzy set theory is proven to be useful and
helpful in vague compactness measurement index.
2. COMPACTNESS MEASUREMENT LIMITATION &
PROBLEMS
The various types of compactness measurement for evaluating
the results of the redistricting plan are from tremendous
endeavor of compactness measurements in redistricting. It really
shows the importance of geographical aspect in redistricting and
how necessary for different techniques are to be used to
measure the compactness and continuity of the district plans.
However, these compactness measurements commonly used
after the redistricting process and usually treated as separately
to redistricting effort. The reason for assessing compactness
and continuity of the redistricting plan is to ensure balance and
fair result. However, current research does not help district
planners to determine which compactness measures to use,
which are effective, and neutral. Therefore, choosing a particular
compactness measure was a special challenge because
previous researchers have proposed over thirty distinct
measures of compactness.
Most of the existing redistricting methods do not primarily
concern on the shape or spatial context and suffering from
problems in implementation because lack of systematic
evaluation, inferior decision making or decision support process.
Compactness measurement for district compactness and
continuity assessment gives an index for assessment and for
decision making of compact district but these methods do not
