為處理單一決策者及群體決策環境下決策者風險偏好的影響，本研究運用增量分析的概念一般化TODIM法(葡萄牙語 Interactive and Multi-criteria Decision Making 的意思)，並擴展至群體決策的環境中，以建構一整合式的多準則群體決策支援模式。本研究除修改傳統TODIM價值函數在損失部分的缺陷外，亦對不同類型準則分別使用線性與非線性價值函數，也針對運用增量分析法後決策者對方案之排序以及群體中每位決策者的相對權重進行整合。其次，對不同序數值轉換為基數值的方法與決策者排序距離矩陣之特徵向量以決定決策者相對權重的方法進行比較與討論。另外，經由模式內價值函數之參數敏感度分析以及不同決策者權重比較也證明了本模式的穩固性。最後，案例說明顯示本整合架構之可行性。

This study aims to generalize TODIM (an acronym in Portuguese of Interactive and Multi-Criteria Decision Making) by incremental analysis (IA) for a risky decision making and extending it to a group decision-making environment. For generalization, two types of scaling effects are overcome. One effect is due to the defect of original TODIM formulation in losses part of the two parts value function, and the criteria with smaller weights will contribute larger dominance values in the computing process. The other effect is derived from aggregating partial dominance measurements among different characteristics of criteria in TODIM while the criteria can be divided into two categories, benefits and costs, for effective resource allocation. In such a way, different types of value functions are considered for reflecting the decision maker’s risk preference. IA is then employed to rank alternatives according to the given cutoff benefit-cost ratio for two accumulated dominance measurements. A fuel buses example is illustrated.
The proposed method is extended to a group decision making environment in which multiple decision makers (DMs) execute the model. The ordinal rank of each DM can be converted to cardinal value through rank sum and regression-like function. In addition, the relative decision power of each DM is taken into account based on the eigenvector of their ranking distance comparison matrix. Later, sensitivity analyses are employed on the different values of the parameters in the value function, the cutoff benefit-cost ratios, and different weights of DMs to demonstrate the robustness of the proposed model for group decision. Furthermore, a number of other MCDM techniques have been compared. The results show that the proposed model is feasible and effective for the demonstrated example under risk.

Contents
CHINESE ABSTRACT	II
ENGLISH ABSTRACT	III
CONTENTS	V
LIST OF TABLES	VII
LIST OF FIGURES	IX
Chapter 1	Introduction	1
1.1	Background and Motivation	1
1.2	Objectives	4
1.3	Structure of This Study	5
Chapter 2	Literature Survey	7
2.1	Prospect Theory	7
2.2	TODIM	9
2.3	Risk Preferences	14
2.4	Incremental Analysis	15
2.5	Conversion of Ordinal Ranking to Cardinal Value	18
2.6	Group Decision Making	19
2.7	Other MCDM Approaches for Comparisons	20
2.8  Summary	24
Chapter 3	The Proposed Approach	25
3.1  Traditional TODIM and the Modification………………………………………….25
3.2  The Assumptions of the Proposed Model	27
3.3  Generalized TODIM Method by IA	27
3.4  Generalized TODIM Method by IA for GDM	33
3.5  Summary	36
Chapter 4	Illustrative Example	38
4.1	The Proposed Model for A Single DM	40
4.2	The Proposed Model for GDM	49
4.3	Comparison of the Proposed Model with Other MCDM Approaches	56
4.4	Summary	63
Chapter 5	Conclusions and Remarks	64
5.1	Conclusions	64
5.2	Remarks	66
References		68

LIST OF TABLES
Table 2-1 Matrix of normalized alternatives scores against criteria	13
Table 3-1 The differences between traditional TODIM and generalized TODIM	……………29
Table 4-1 Performance measures of alternative buses	39
Table 4-2 Weights of criteria provided by DMs in the group……………………….	40
Table 4-3 The dominance measurements of benefit/cost criteria for alternatives using 
generalized TODIM……….....................................................................................42

Table 4-4 Incremental analysis based on the dominance measurements of generalized
TODIM.……………………...................................................................................43

Table 4-5 The ranking results of the proposed model and other related methods.	…………..44
Table 4-6 Comparison of sensitivity analysis of the proposed model and TODIM	46
Table 4-7 The relationship of the weight and standard deviation of partial dominance
values among alternatives for each criterion in traditional TODIM……………....48
Table 4-8 Ranking of alternative buses using generalized TODIM with IA	50
Table 4-9 Cardinal data converted from ranking results of IA	51
Table 4-10 Pairwise ranking distance comparison matrix of DMs and relative importance weights………………...........................................................................................52
Table 4-11 Weighted performance value and ranking of DMs	53
Table 4-12 Ranking results obtained using the proposed GDM model compared with
three weighting vectors among DMs……………………………………………..54

Table 4-13 The ranked lists from different aspects of λ, α, and β………................................55
Table 4-14 The comparison of different approaches	57
Table 4-15 Selection	60

LIST OF FIGURES
Figure 1-1 The structure of this study	 6
Figure 2-1 S-shaped value function of prospect theory	 9
Figure 2-2 IA procedure	18
Figure 3-1 The value functions of the generalized TODIM	28
Figure 3-2 The proposed procedure for the MCDM problem	……………………33
Figure 3-3 The proposed procedure for the GDM problem	……………………36
Figure 4-1 Ranking results of different cutoff benefit-cost ratios……………………………47
Figure 4-2 The inverse relationship of the weight and standard deviation of partial dominance values among alternatives for each criterion in traditionalTODIM……………...48

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