||Generalized TODIM by Incremental Analysis and Its Extension
||Doctoral Program, Department of Management Sciences
||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.
CHINESE ABSTRACT II
ENGLISH ABSTRACT III
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
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
Table 4-4 Incremental analysis based on the dominance measurements of generalized
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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