ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS", Bangkok, May 23-25, 2001 
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used to formalize the gray area in order to specifically express 
and also never ignore the gray area. 
Linguistic terms which have been found intuitively easy to use 
[4] are used to represent the decision maker’s subjective 
assessment on the compactness measurement index. A term 
set of linguistic for each compactness measurement index (CMI) 
is {Very Poor (VP), Poor (P), Fair (F), Good (G), Very Good (G)}, 
defined in Figure 2. 0. The weighing vector for the compactness 
evaluation criteria will be directly given by the decision maker or 
obtained by using pairwise comparison. Meanwhile, the term set 
used for the weighing vector is {Least Important (LTI), Less 
Important (LSI), Important (I), More Important (MEI), Most 
Important (MTI), Most Important (MTI)}, defined as in Figure 3.0. 
H(x) 
0 3 5 7 9 X 
Figure 2. 0: Membership functions, O(x) and the linguitics terms 
for CMI, x 
P(x) 
Figure 3.0 : Membership function, O(x) and the linguistic terms 
used by the weighing vector, X 
3.3 Decision Support with FMCDM 
The proposed integrated model is able to consider multiple 
compactness measurements as a measurement instruments to 
ensure optimal compact district. However, the compactness 
measurement provides numerical index, which is vague and 
may be incomplete. Therefore, Fuzzy Multiple Criteria Decision 
Making (FMCDM) will be able to provide a solution for the 
problem s mentioned. Therefore, multiple compactness 
measurement will used to produce an integrated compactness 
index that is able to cope with fuzziness to measure the 
geographical aspect of the district plan. Multi Criteria Decision 
Making (MCDM) deals with problem of helping the decision 
maker to choose the best alternatives, according to several 
criteria (Vails, 2000). This approach is used to solve complex 
shape based redistricting problems in a systematic, consistent 
and more productive way because it may enhance the degree of 
conformity and coherence in the decision process [3]. 
Meanwhile, the fuzziness concept is used to solve the 
subjectiveness and vagueness for deciding the compactness 
assessment index. Therefore, fuzzy sets theory to MCDM 
models is used to provides an effective way of dealing with the 
subjectiveness and vagueness of decision making process for 
the general multiple criteria shape based redistricting problems. 
This method is to support a systematic decision making for 
several reasons [7]. First, the information and knowledge for the 
redistricting decisions is incomplete, uncertain or imprecise or 
even inconsistent state clearly for this but the information 
overload is still increasing. Second, there are also multiple 
conflicting goals and multiple different type of constraint. 
Therefore, the proposed redistricting environment will be the 
integration of FMCDM in GIS environment to enhance the 
shape-based redistricting process. Indeed, FMCDM is an 
Operation Research (OR) technology [5] that can face the 
complexity of the environment, which strategic decisions are 
needed especially like the redistricting problems. In multiple 
criteria program, redistricting application functions are 
established to measure the degree of fulfillment of the decision 
maker’s requirements about the goal function and are 
extensively used in the process of finding “good compromise” 
solution [3]. For district planners, the requirements in 
redistricting application include the achievement of goals on 
compactness, nearness to an ideal point on the application 
dependent factor, and other satisfaction. According to Fuller and 
Carlsson, one of the earliest practical application of FMCDM is a 
commercial application for evaluation of the credit-worthiness of 
credit card applicants [3]. 
The FMCDM method to be used in this research is Fuzzy 
Analytical Hierarchy Process or Fuzzy AHP. Analytical Hierarchy 
Process is a multi criteria method which uses hierarchic 
structures to represent a decision problem and then develops 
priorities for the factors based on decision maker’s judgement. It 
has been widely used to solve complicated, unstructured 
decision problems and thus it should be concerned with the 
processing of fuzzy information. As it is difficult to get exact 
ratios for a pair of factors considered, fuzzy ratios for the relative 
significant may incorporates the natural feelings of human 
beings. In other words, fuzzy theory is effective when the 
situation contains fuzziness from human subjectivity in 
redistricting functions. Indeed, Fuzzy AHP method was 
discussed and being used for ranking of Indian Coals in 
industrial use [8], rate and ranking the disability [9] and also 
assessing risk of cumulative trauma disorders [10]. 
Consequently, this method is proven to be a useful method in 
enhancing the redistricting process because the AHP allows 
decision makers to express their judgements of pairwise 
comparison in fuzzy ratios for indicating its importance in the 
aggregation procedure. In addition, the fuzzy ratios is able to 
avoid unbalanced scale of estimations and its ability to 
adequately handle the uncertainty and imprecision associated 
with the mapping of the decision makers’ perception to a crisp 
number [4]. Fuzzy value from the SOR mentioned will be 
integrated into the model for the decision making process in the 
integrated model. Two of the compactness measurements can 
be taken into account according to the user’s option. Indeed, 
compactness measurement to be used here can be customized 
to any other measures, which will be more relevant to different 
redistricting goals because the primary aim of this research is 
mainly to provide a metaphor to integrate FMCDM in GIS for 
shape-based redistricting by using the multiple compactness 
measurements. 
The general shape-based redistricting decision problem usually 
consists of (a) a number of alternatives, which refer to the 
individual district, denoted as A t (i = 1, 2, ..., n), (b) a set of 
evaluation criteria C y (j = 1, 2, .... m) which some of them may 
refer to the compactness measurements, (c) a qualitative or 
quantitative assessment^ (/ = 1, 2, ..., n; j = 1, 2, ... , m) 
(referred to as performance ratings) representing the 
performance of each alternative Ai with respect to each criterion