Fuzzy Attribute Expansion Method for Multiple Attribute Decision-Making with Partial Attribute Values and Weights Unknown and Its Applications
Abstract
:1. Introduction
2. Basic Definitions
- (a)
- (b)
- ,
- (c)
- ,
- (a)
- ,
- (b)
- ,,
- (a)
- ,
- (b)
- ,
- (c)
- ,,
3. Problem
- (a)
- The length of is , ;
- (b)
- The sequence of attribute weights is ;
- (c)
- Evaluation value of falls into the interval , the greater the evaluation value is, the higher the evaluation is.
- (d)
- The evaluation values are as similar to those obtained under the condition that some UFAs are given as possible.
4. Geometric Analysis of PAS, MAS, and FAMS
5. The Fuzzy Attribute Expansion Method
5.1. The Technique to Approximate Estimate UFAs Based on Interpolation
5.2. The Technique to Generate the Final Evaluation Based on Attribute Weight Reconfiguration
6. Applications
6.1. Applications for Regression
6.2. Applications for Clustering
6.3. Applications for Power Quality Evaluation
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Regression Model | A 1 | HL (Train/Test) | MSE (Train/Test) | EI (Train/Test) | NUFA2 |
---|---|---|---|---|---|
SVMR | 0 | 2.6426/2.5052 | 18.4283/18.3963 | 2.3938/2.3395 | / |
1 | 2.6427/2.4991 | 18.3377/18.3808 | 2.3949/2.3379 | <1.08:0.08:2.92> | |
GKR-1 | 0 | 2.1724/2.2637 | 15.5750/17.2569 | 1.9958/2.0781 | / |
1 | 2.1362/2.1400 | 15.4048/16.1185 | 1.9793/1.9573 | <1.08:0.8:2.68> | |
GKR-2 | 0 | 2.0406/2.2523 | 12.8566/17.0757 | / | / |
1 | 1.9960/2.0937 | 12.5828/15.6837 | / | <1.08:0.8:2.68> |
Regression Model | A 1 | HL (Train/Test) | MSE (Train/Test) | EI (Train/Test) | NUFA2 |
---|---|---|---|---|---|
SVMR | 0 | 2.0199/1.8340 | 12.5788/10.6975 | 1.8338/1.6461 | / |
1 | 2.0220/1.8295 | 12.4889/10.5811 | 1.8323/1.6459 | <1.08:0.08:3.96> | |
GKR-1 | 0 | 1.7104/1.7270 | 11.0732/13.1882 | 1.5813/1.6434 | / |
1 | 1.5242/1.5924 | 10.5474/10.5426 | 1.4230/1.4778 | <1.8:1:3.8> | |
GKR-2 | 0 | 1.4146/1.7246 | 7.1309/11.8654 | / | / |
1 | 1.1562/1.5241 | 5.9034/9.0240 | / | <1.8:1:3.8> |
Clustering Method | A 1 | AR (Worst/Mean/Best) | RI (Worst/Mean/Best) | NMI (Worst/Mean/Best) | NUFA |
---|---|---|---|---|---|
FCM | 0 | 0.8800/0.8879/0.8933 | 0.8679/0.8748/0.8797 | 0.7225/0.7328/0.743 | / |
1 | 0.9200/0.9200/0.9200 | 0.9055/0.9055/0.9055 | 0.7855/0.7855/0.785 | <1.8:0.5:3.8> | |
K-means | 0 | 0.5800/0.7822/0.8867 | 0.7214/0.8210/0.8737 | 0.5927/0.6830/0.741 | / |
1 | 0.5067/0.8373/0.9533 | 0.7204/0.8648/0.9417 | 0.6011/0.7653/0.846 | <1.8:0.5:3.8> | |
K-medoids | 0 | 0.9000/0.9040/0.9067 | 0.8859/0.8897/0.8923 | 0.7578/0.7596/0.761 | / |
1 | 0.9333/0.9333/0.9333 | 0.9195/0.9195/0.9135 | 0.8038/0.8038/0.804 | <1.8:0.5:3.8> |
Measurable Attributes | Node1 | Node2 | Node3 | Node4 | Node5 |
---|---|---|---|---|---|
(Frequency deviation) | 0.0922 | 0.1562 | 0.1180 | 0.1787 | 0.1892 |
(Voltage deviation) | 3.2120 | 6.6800 | 4.3500 | 5.3300 | 4.2200 |
(Voltage sag) | 79.6300 | 15.8900 | 51.5600 | 58.5600 | 48.6300 |
(Three phase imbalance) | 0.8300 | 1.3600 | 1.3500 | 1.7400 | 1.8300 |
(Voltage fluctuation) | 1.3300 | 1.5300 | 1.9500 | 1.3700 | 1.5800 |
(Voltage flicker) | 0.4730 | 0.8470 | 0.6340 | 0.8260 | 0.8280 |
(Voltage harmonics) | 1.7200 | 4.3800 | 2.6700 | 3.3600 | 4.5700 |
(Unreliability index) | 0.1670 | 0.2380 | 0.2040 | 0.2600 | 0.2360 |
(Unserviceable index) | 0.1680 | 0.2870 | 0.1360 | 0.3160 | 0.2170 |
Node1 | Node2 | Node3 | Node4 | Node5 |
---|---|---|---|---|
0.1309 | 0.6720 | 0.4262 | 0.7405 | 0.7054 |
Methods | Node1 | Node2 | Node3 | Node4 | Node5 | Hamming Distance |
---|---|---|---|---|---|---|
Traditional | 0.2000 | 0.5025 | 0.5347 | 0.6293 | 0.6415 | 0.8 |
Proposed | 0.1063 | 0.6281 | 0.4757 | 0.6884 | 0.6436 | 0 |
Methods | Node1 | Node2 | Node3 | Node4 | Node5 | Hamming Distance |
---|---|---|---|---|---|---|
Traditional | 0 | 0.6281 | 0.5285 | 0.6192 | 0.6735 | 0.6 |
Proposed | 0 | 0.6650 | 0.5133 | 0.6242 | 0.6354 | 0.4 |
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Zhuo, J.; Shi, W.; Lan, Y. Fuzzy Attribute Expansion Method for Multiple Attribute Decision-Making with Partial Attribute Values and Weights Unknown and Its Applications. Symmetry 2018, 10, 717. https://doi.org/10.3390/sym10120717
Zhuo J, Shi W, Lan Y. Fuzzy Attribute Expansion Method for Multiple Attribute Decision-Making with Partial Attribute Values and Weights Unknown and Its Applications. Symmetry. 2018; 10(12):717. https://doi.org/10.3390/sym10120717
Chicago/Turabian StyleZhuo, Jinbao, Weifeng Shi, and Ying Lan. 2018. "Fuzzy Attribute Expansion Method for Multiple Attribute Decision-Making with Partial Attribute Values and Weights Unknown and Its Applications" Symmetry 10, no. 12: 717. https://doi.org/10.3390/sym10120717