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

ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS", Bangkok, May 23-25, 2001
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.
0 3 5 7 9 X
Figure 2. 0: Membership functions, O(x) and the linguitics terms
for CMI, 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
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