ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001 
304 
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