臺灣博碩士論文加值系統

在多屬性決策中，如何合理、適當的來衡量屬性權重是非常重要的問題，因為不同的屬性權重分配，往往會造成最後所得到的決策結果的不同。自從學者提出直覺模糊集合之後，近年開始有學者應用直覺模糊集合至多屬性決策的領域，來幫助我們可以得到更準確的資料，但也因此造成我們所得到的資料，是更加複雜、更加難以處理的，而資料本身也充滿更多的不確定性，因此如何衡量資料本身的可信度相對是非常重要的問題，然而，在過去的研究中，鮮少有學者討論這部份的問題，因此本研究運用直覺模糊熵的特性，發展出一種新的客觀權重求解方法，來幫助我們衡量屬性的資訊重要程度。再者，過去有許多學者運用不同的理論架構提出很多不同的直覺模糊熵測量方法，而本研究也一併探討各個方法之間存在的差異性。而根據實驗結果，我們了解到各種測量方法之間，存在著很大的差異性，即使是源自相同理論的測量方法，也有相當程度的差異存在，此外，由實驗結果我們也了解到，屬性數和方案數也會對於公式之間的差異程度造成明顯的影響。

In Multiple Attribute Decision Making (MADM), it is important to properly assess the attribute weight, because different weight result would often cause entirely different decision result. Furthermore, after the IFS was applied to solve MADM problems, it causes our data and decision matrix get more complex and contain more uncertainty, and therefore it is relatively important to make sure of the credibility of data itself. However, there is little investigation on MADM with the credibility of data being explicitly taken into account in the past. In our research, we propose a new objective weight method by using IF entropy measures for MADM under intuitionistic fuzzy environment. We utilize the nature of IF entropy to assess the attribute weight based on the credibility of data. Moreover, there were many IF entropy measures which were originated with different theories, and we also investigate the differences among those varied measures. According to the experiment result, the differences undoubtedly exist among those measures. Even the measures which were originated from the same theory also contain variation among them. Besides, we also understand the number of attributes and alternatives would influence the degree of difference among those measures.

Contents
Chpater I Introduction…………………………………………………..……1
1.1 Motivation…………………………………………………………………..1
1.2 Objectives ………………………………………………………………..…2
Chpater II Literature Review……………………………………………….…3
2.1 Multiple Attribute Decision Making……………………………………..…3
2.2 Fuzzy Multiple Attributes Decision Making……………………………..…4
2.3 MADM Based on Intuitionistic Fuzzy Set………………………………4
2.4 Methods for Assessing Attribute Weights……………………………….7
2.4.1 Methods for Assessing Subjective Weights……………………………7
2.4.2 Methods for Assessing Objective Weights………………………....9
2.4.3 Compromise Methods for Assessing Attribute Weights……………...11
Chpater III Entropy Measures for Intuitionisitc Fuzzy Sets………………….13
3.1 Intuitionistic Fuzzy Sets and Interval-valued Fuzzy Sets…………………13
3.1.1 Intuitionistic Fuzzy Sets……………………………………………...13
3.1.2 Interval-valued Fuzzy Sets…………………………………………...13
3.2 Fuzzy Entropy on Fuzzy Sets……………………………………………...14
3.3 Entropy Measure on Intuitionistic Fuzzy Sets……………………….........14
3.4 Summary of IF Entropy Measures………………………………………...21
Chpater IV Research Method…………………………………………………34
4.1 Algorithm………………………………………………………………….34
4.2 Numerical Example………………………………………………………..36
Chpater V Experiment Analysis…………………………………………..…43
5.1 Data Analysis………………………………………………………………43
5.2 Experiment Analysis of Group 1…………………………………..……44
5.2.1 Analysis of Average r-values of Group 1…………………….………44
5.2.2 Analysis of Average ρ-values of Group 1…………………………….47
5.2.3 Analysis of Contradiction Rates of Group 1………………………49
5.2.4 Analysis of Inversion Rates of Group 1……………………………..52
5.2.5 Analysis of Consistency Rates of Group 1…………………………...54
5.3 Experiment Analysis of Group 2……………………………………….57
5.3.1 Analysis of Average r-values of Group 2…………………………….57
5.3.2 Analysis of Average ρ-values of Group 2…………………………….58
5.3.3 Analysis of Contradiction Rates of Group 2………………………60
5.3.4 Analysis of Inversion Rates of Group 2……………………………...61
5.3.5 Analysis of Consistency Rates of group 2…………………………...63
5.4 Experiment Analysis of Group 3………………………………………......64
5.4.1 Analysis of Average r-values of Group 3…………………………….64
5.4.2 Analysis of Average ρ-values of Group 3…………………………….65
5.4.3 Analysis of Contradiction Rates of Group 3………………………66
5.4.4 Analysis of Inversion Rates of Group 3……………………………..68
5.4.5 Analysis of Consistency Rates of group 3………………………….69
5.5 Experiment Analysis of Group 4……………………………………….70
5.5.1 Analysis of Average r-values of Group 4…………………………….70
5.5.2 Analysis of Average ρ-values of Group 4…………………………….73
5.5.3 Analysis of Contradiction Rates of Group 4………………………75
5.5.4 Analysis of Inversion Rates of Group 4……………………………..78
5.5.5 Analysis of Consistency Rates of Group 4…………………………...80
5.6 Experiment Analysis among Four Groups………………………………...82
5.6.1 Analysis of Average r-values among Four Groups…………………..83
5.6.2 Analysis of Average ρ-values among Four Groups…………………..85
5.6.3 Analysis of Contradiction Rates among Four Group………………...87
5.6.4 Analysis of Inversion Rates among Four Groups……………………88
5.6.5 Analysis of Consistency Rates among Four Groups…………………90
5.7 Summarization of Experiment Results…………………………………….92
5.8 Second-order Regression Model…………………………………………..95
5.7.1 Regression Analysis of Group 1…………………………………...96
5.7.2 Regression Analysis of Group 2……………………………….......98
5.7.3 Regression Analysis of Group 3………………………………….100
5.7.4 Regression Analysis of Group 4………………………………….102
5.7.5 Regression Analysis of the Comparisons among Four Groups……..104
5.9 Summary of Analyze……………………………………………….…..107
Chpater VI Conclusions………………………………………………………109
6.1 Discussions….……………………………………………………………109
6.2 Future Research…………………………………………………………..109
Reference ………………………………………………………………………110






List of Figures
Figure 3.1 Test of β values of G4.2…...…………………………………….22
Figure 3.2 Test of k values of G1.2...……………………………………….23
Figure 3.3 Test of α values of G4.1………………………..…………….….24
Figure 5.1 Average r-value of group 1…………………………………………..45
Figure 5.2 Average ρ-value of group 1 …………………………………….…48
Figure 5.3 Contradiction rate of group 1………………………………...……50
Figure 5.4 Inversion rate of group 1………………………………………….…..53
Figure 5.5 Consistency rate of group 1………………………………………..55
Figure 5.6 Average r-value of group 2…………………………………..………57
Figure 5.7 Average ρ-value of group 2………………………………………..…59
Figure 5.8 Contradiction rate of group 2………………………………….……...60
Figure 5.9 Inversion rate of group 2……………………………………….…..…62
Figure 5.10 Consistency rate of group 2………………………………….…….63
Figure 5.11 Average r-value of group 3………………………………………..…65
Figure 5.12 Average ρ-value of group 3………………………………………..…66
Figure 5.13 Contradiction rate of group 3……………………………………...…67
Figure 5.14 Inversion rate of group 3…………………………………………..….68
Figure 5.15 Consistency rate of group 3……………………………………….70
Figure 5.16 Average r-value of group 4………………………………………..…71
Figure 5.17 Average ρ-value of group 4……………………………………..….73
Figure 5.18 Contradiction rate of group 4……………………………………...76
Figure 5.19 Inversion rate of group 4……………………………………………..78
Figure 5.20 Consistency rate of group 4……………………………………..…81
Figure 5.21 Average r-value among four groups……………………………….…84
Figure 5.22 Average ρ-value among four groups…………………………………86
Figure 5.23 Contradiction rate among four groups………………………………..87
Figure 5.24 Inversion rate among four groups……………………………………89
Figure 5.25 Consistency rate among four groups…………………………………91


List of Tables
Table 3.1 Scholar and IF entropy measures…………………………………….……25
Table 3.2 The numbered IF entropy measures…………………………………….…28
Table 3.3 The IF entropy measures for experiment……………………………….…31
Table 4.1 Decision matrix in the numerical example……………………………...…38
Table 4.2 IF entropy values are calculated by using A1………………...……………39
Table 4.3 The normalized IF entropy values by using A1……………...…………39
Table 4.4 The normalized entropy values for decision matrix by using A1…….……39
Table 4.5 The weights of each attribute by using A1………………………………...40
Table 4.6 The weight values produced by six different formulas……………………40
Table 4.7 The weight rank of the attribute…………………………………………...41
Table 4.8 The Pearson and Spearman rank correlation……………………………....41
Table 5.1 The average consistency rate of the equations…………………….….83
Table 5.2 The total average contradiction rate of each measure…………………......92
Table 5.3 Total average inversion rate of each measure…………………………..…93
Table 5.4 Average contradiction, inversion and consistency rate among four groups.93
Table 5.5 The total average of average ρ-values of each comparison…………..……94
Table 5.6 The regression result of group 1………………………………………..…97
Table 5.7 The regression result of group 2………..………………………………..99
Table 5.8 The regression result of group 3………………………….........................101
Table 5.9 The regression result of group 4………………………………………….103
Table 5.10 The regression result of the comparisons among 4 groups…..................105

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