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

Chen, Jun

Bibliographic data

Monograph

Persistent identifier:: 856566209

Author:: Chen, Jun

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

Sub title:: May 23 - 25, 2001, Bangkok, Thailand

Scope:: VI, 434 Seiten

Year of publication:: 2001

Place of publication:: Pathumthani, Thailand

Publisher of the original:: AIT

Identifier (digital):: 856566209

Illustration:: Illustrationen, Diagramme, Karten

Language:: English

Usage licence:: Attribution 4.0 International (CC BY 4.0)

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2016

Document type:: Monograph

Collection:: Earth sciences

Chapter

Title:: INTEGRATION OF COMPACTNESS MEASUREMENT METHODS USING FUZZY MULTICRITERIA DECISION MAKING : A NEW APPROACH FOR COMPACTNESS MEASUREMENT IN SHAPE BASED REDISTRICTING ALGORITHM. Yinchai WANG

Document type:: Monograph

Structure type:: Chapter

ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS", Bangkok, May 23-25, 2001 One of the significant improvements of the new proposed redistricting algorithm is the availability of the parameter to show the attitude to risk, a and level of confidence, X of the district planner. These parameters act as observation parameter, which aim to analyze the decision-making behavior of the decision makers. Therefore, we have defined the decision makers based on their attitude to risk into three different groups that are the optimistic, moderate or pessimistic decision makers. 3.4 Optimization by Dynamic Programming The redistricting problems are treated as similar to the knapsack problem, which is maximization or minimization of a value. For example, a thief robbing a safe finds it filled with N items of various size and value but bag has only limited capacity (M). In contrast, getting compact district plan means to calculate the best combination of individual district for all district size up to total district plan size. In other words, the district plan is a plan that consists of many districts with different shape. Therefore, the adopted implementation method in this research is Dynamic Programming(DP) which is commonly used to solve the knapsack problem. The method is chosen based on two main reasons. First, DP takes time as the horizon and calculates the least cost path in the interval. It is similar to the redistricting process which ask for optimal compact district, so DP can build a good model in a bottom-up technique to solve redistricting problems. It allows for the breaking up of all problems into a sequence of easier subproblems which are then evaluated by stages and has the power to determine the optimal solution by solving each of these stages optimality [11]. Second, redistricting decisions is usually accompanied with many complicated considerations, so these might be numerical constraints or some constraints which were the experience of the experts. These constraints are difficult to solve by nonlinear programming or other methods but can be easily incorporated and solved by the DP method. In addition, when integrate with FMCDM, these constraints can even be systematically analyzed and solved. 4. RESULTS AND ANALYSIS The evaluation of the developed shape based redistricting algorithm using forest blocking application as an prototype focuses on the applications and limitations of incorporating an enhanced compactness index based on multiple compactness measurement into redistricting technique by using fuzzy multiple criteria decision making. Overall performance of the developed shape based redistricting algorithm is evaluated using statistical tests. The statistical tests were applied on different conditions in order to find out the performance of the developed shape based redistricting algorithm under different circumstances. These tests used for evaluation are referring to existing standard use to define a district plan. For example, a plan’s compactness is defined as the mean compactness of its districts used in Iowa and in Michigan in United State for political redistricting [2]. Besides, other research mentioned that its least compact district determines the compactness of a plan. Consequently, in this study, statistical test that include Mean, Mean Deviation, Maximum, Minimum and their Difference of compactness indices for its districts is used to determine the compactness evaluation of a district Plan. There were three main areas of evaluations and tests was carried out on the redistricting algorithm: (a) performance evaluation and comparison on district plan produced with and without the enhanced redistricting algorithm, (b) result and analysis on the advance FMCDM component, (c) result and analysis with respect the different input variable like interval to calculate slope and also the restricted boundaries such as river and license boundary using prototype. From the evaluation process shown that the proposed method has the ability to consider multiple criteria to ensure the compactness is within optimality in producing district plan. Although there is a necessary to have a precise understand on the shape optimal rule or the linguistic terms’ definition of the most compact district, the scheme able to produce a Enhanced Compactness Index in order to represent the performance of the district within the district plan. Besides, it is definitely going to give adequate reflection of the district planner toward risk and their confidence in their subjectivity assessment. In conclusion, the enhanced redistricting algorithm really shows ability to shape based redistricting scheme is going to give better performance to draw or redraw district plan with optimal compactness. The applicability of the methods is proven effective. An Integrated Compactness Index had been successfully calculated and incorporated into redistricting technique that discussed. This compactness assessment index is more descriptive and able to incorporate with natural feelings of district planners. Natural feelings here may include their confidence and their attitude to risk. The shape compactness information has been modeled flexibly by utilizing the Fuzzy Multiple Criteria Decision Making approach like Fuzzy AHP. The Fuzzy AHP approach allows the integration of both Application Dependent and Application Independent factors to be considered in the redistricting application. The consideration of Application Dependent criteria is compulsory whereby the consideration of Application Independent criteria here is the more unique factors to ensure the optimality of shape compactness. Besides, the integrated shape-based redistricting technique is able to cope with fuzziness in the compactness assessment index. The triangular fuzzy number used to define the decision matrix and weight matrix able to help to define the fuzziness of optimality of the compactness. The integration of multiple compactness measurement methods in enhanced redistricting algorithm able to gather the strengths of particular method and at the same time to reduce or minimize the weaknesses or lacks of other method. Manipulating the weight matrix that represents the importance of a particular measurement accomplishes it. Then, these weight vectors will then contribute to the enhanced compactness index, which will incorporate into the redistricting process. A prototype is built based on the conceptual design of the redistricting algorithm. The prototype demonstrated the application of redistricting algorithm developed. It also allowed the testing and evaluation to be implemented. The prototype managed to demonstrate the concept of the integration and the incorporation in the redistricting algorithm. Later, overall performance of the developed redistricting algorithm is evaluated using statistics tests. The statistics tests are applied on different condition in order to find out the performance of the developed shape based redistricting algorithm under different circumstances. The approach developed clearly has its advantages. These advantages include (a) better modeling of the uncertainty and imprecision associated with the fuzzy triangular number, (b) Cognitively less demanding on the district planner, and (c) adequate reflection of the district planner’s attitude towards risk and their degrees of confidence in their subjective assessment. Real experience in applying the approach in selecting the most appropriate district plan in the prototype has reinforced these findings. The incorporation of shape information sources has enhanced the redistricting techniques by utilizing more sources of information. As a result, the redistricting technique no longer based on the application dependent information only. The incorporation is proven to redraw district boundary effectively when there is more than one criterion. 5. CONCLUSION This research has contributed to the improvement of redistricting

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