Performance Evaluation of Automobile Fuel Consumption Using a Fuzzy-Based Granular Model with Coverage and Specificity
Abstract
:1. Introduction
2. GM
2.1. CFCM Clustering
- [Step 1]
- The number of linguistic contexts (2 to 20) and the number of clusters to be created in each context (2 to 20) was selected. The belonging matrix was initialized to an arbitrary value between 0 and 1.
- [Step 2]
- A linguistic context was created using a triangular membership function that was evenly distributed in the output space.
- [Step 3]
- For each context, the cluster center and the belonging value were calculated.
- [Step 4]
- The objective function was calculated, as given by Equation (6), and if the degree of improvement obtained through the previous iteration wasless than the threshold value, the process was stopped.
- [Step 5]
- The new membership matrix U was calculated from Equation (3), and control was returned to [Step 3].
2.2. Structure of the GM
2.3. Structure of the GM
3. Performance Evaluation Method
3.1. Performance Evaluation Method Suitable for the GM
3.1.1. Coverage
3.1.2. Specificity
4. Experimental Results
4.1. Auto MPG Database
4.2. Experiment Method and Analysis of Results
5. Discussion
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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PI (Performance Index) Methods | Equations | |
---|---|---|
Hu [30] | Coverage | |
Specificity | ||
Performance index | ||
Zhu [31] | Coverage | |
Specificity | ||
Performance index | ||
Galaviz [32] | Coverage | |
Specificity | ||
Performance index |
Algorithm | Performance Evaluation Method | ||
---|---|---|---|
Granular Model | RMSE | ||
Number of Contexts | Number of Clusters | Training RMSE | Testing RMSE |
10 | 2 | 3.96 | 4.15 |
3 | 3.98 | 4.18 | |
4 | 3.69 | 3.91 | |
5 | 3.72 | 3.90 | |
6 | 3.90 | 4.10 | |
7 | 3.89 | 4.07 | |
8 | 3.98 | 4.09 | |
9 | 3.95 | 4.15 | |
10 | 3.54 | 4.17 |
Algorithm | Performance Evaluation Method | ||
---|---|---|---|
Granular Model | RMSE | ||
Number of Contexts | Number of Clusters | Training RMSE | Testing RMSE |
10 | 2 | 3.75 | 3.79 |
3 | 3.65 | 3.80 | |
4 | 3.71 | 3.73 | |
5 | 3.95 | 3.93 | |
6 | 3.79 | 4.13 | |
7 | 3.87 | 4.12 | |
8 | 3.75 | 3.95 | |
9 | 3.89 | 4.31 | |
10 | 3.78 | 4.41 |
Granular Model That Evenly Divides Linguistic Context (No. Context = 10) | |||
---|---|---|---|
Number of Clusters | Coverage | Specificity | Performance Index |
2 | 0.72 | 2.35 | 1.70 |
3 | 0.69 | 2.35 | 1.63 |
4 | 0.72 | 2.35 | 1.69 |
5 | 0.71 | 2.35 | 1.68 |
6 | 0.69 | 2.35 | 1.61 |
7 | 0.68 | 2.35 | 1.60 |
8 | 0.70 | 2.35 | 1.64 |
9 | 0.72 | 2.35 | 1.70 |
10 | 0.68 | 2.35 | 1.61 |
Granular Model That Flexibly Divides Linguistic Context (No. Context = 10) | |||
---|---|---|---|
Number of Clusters | Coverage | Specificity | Performance Index |
2 | 0.74 | 12.39 | 9.23 |
3 | 0.76 | 15.36 | 11.68 |
4 | 0.69 | 13.69 | 9.50 |
5 | 0.71 | 16.8 | 11.91 |
6 | 0.75 | 16.5 | 12.38 |
7 | 0.70 | 17.53 | 12.26 |
8 | 0.74 | 18.18 | 13.45 |
9 | 0.66 | 17.77 | 11.78 |
10 | 0.64 | 19.64 | 12.63 |
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Yeom, C.-U.; Kwak, K.-C. Performance Evaluation of Automobile Fuel Consumption Using a Fuzzy-Based Granular Model with Coverage and Specificity. Symmetry 2019, 11, 1480. https://doi.org/10.3390/sym11121480
Yeom C-U, Kwak K-C. Performance Evaluation of Automobile Fuel Consumption Using a Fuzzy-Based Granular Model with Coverage and Specificity. Symmetry. 2019; 11(12):1480. https://doi.org/10.3390/sym11121480
Chicago/Turabian StyleYeom, Chan-Uk, and Keun-Chang Kwak. 2019. "Performance Evaluation of Automobile Fuel Consumption Using a Fuzzy-Based Granular Model with Coverage and Specificity" Symmetry 11, no. 12: 1480. https://doi.org/10.3390/sym11121480