Intelligent Decision Framework for Booster Fan Optimization in Underground Coal Mines: Hybrid Spherical Fuzzy-Cloud Model Approach Enhancing Ventilation Safety and Operational Efficiency
Abstract
1. Introduction
2. Methodology Framework
2.1. Analytic Hierarchy Process
- (1)
- Establishing the hierarchical structure
- (2)
- Expert system evaluation
- (3)
- Constructing the judgment matrix
- (4)
- Calculation of the weight vector
- (5)
- Consistency test
- (6)
- Obtainment of the overall weights of the indicators
2.2. Complex Spherical Fuzzy Number
- (1)
- Basic concepts
- (2)
- Scoring function
2.3. Cloud Model
2.4. Expert Decision Making Based on Fuzzy Theory
3. Introduction to the Study Area
4. Case Application of the Method
4.1. Determining Indicator Weights (AHP)
- (1)
- Establishing the hierarchical structure
- (2)
- Obtaining the expert judgment matrix
- (3)
- Calculation of indicator weights
- (4)
- Consistency test
- (5)
- Analysis of comprehensive indicator weights
4.2. Fan Solution Selection Based on Complex Spherical Fuzzy Theory
- (1)
- Solution evaluation based on expert system
- (2)
- Fuzzy information transformation
- (3)
- Solution selection
4.3. Analysis of Alternative Indicators Based on Cloud Model Theory
- (1)
- Evaluation reference cloud
- (2)
- Analysis of solution indicators
5. Conclusions
- (1)
- A booster fan solution evaluation system based on the improved AHP was established, further determining the weights of the indicators involved in the evaluation and extracting the decision preferences of the experts;
- (2)
- A booster fan solution optimization model based on the complex spherical fuzzy theory was established, and the effectiveness of the model was validated through a comparison with related studies;
- (3)
- A risk analysis and optimization model for booster fan solution indicators based on the cloud model theory was established. The model visually presented the rich risk information and optimization potential of the solution indicators through cloud droplets, providing valuable insights for solution optimization.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A. Expert Evaluation Data
Indicator | Solutions | E1 | E2 | E2 |
---|---|---|---|---|
S1 | BF1 | V | IV | IV |
BF2 | IV | IV | IV | |
BF3 | III | III | III | |
BF4 | III | III | III | |
S2 | BF1 | III | V | V |
BF2 | III | IV | III | |
BF3 | III | III | III | |
BF4 | II | III | III | |
S3 | BF1 | II | III | IV |
BF2 | III | IV | III | |
BF3 | I | III | III | |
BF4 | II | IV | III | |
S4 | BF1 | III | IV | V |
BF2 | III | IV | IV | |
BF3 | III | III | II | |
BF4 | III | III | III | |
S5 | BF1 | III | III | III |
BF2 | III | III | IV | |
BF3 | III | III | II | |
BF4 | II | II | II | |
S6 | BF1 | III | II | II |
BF2 | II | II | II | |
BF3 | III | III | IV | |
BF4 | III | II | III | |
S7 | BF1 | V | III | III |
BF2 | III | III | IV | |
BF3 | V | IV | IV | |
BF4 | III | IV | III | |
S8 | BF1 | II | II | V |
BF2 | I | II | III | |
BF3 | II | II | II | |
BF4 | II | II | II | |
S9 | BF1 | I | II | II |
BF2 | I | II | II | |
BF3 | I | II | II | |
BF4 | I | II | II | |
S10 | BF1 | III | V | IV |
BF2 | III | III | III | |
BF3 | III | IV | III | |
BF4 | III | IV | III |
Indicator | Solutions | E1 | E2 | E2 |
---|---|---|---|---|
S1 | BF1 | 0.113 | 0.131 | 0.131 |
BF2 | 0.131 | 0.131 | 0.131 | |
BF3 | 0.395 | 0.395 | 0.395 | |
BF4 | 0.395 | 0.395 | 0.395 | |
S2 | BF1 | 0.395 | 0.113 | 0.113 |
BF2 | 0.395 | 0.131 | 0.395 | |
BF3 | 0.395 | 0.395 | 0.395 | |
BF4 | 0.578 | 0.395 | 0.395 | |
S3 | BF1 | 0.578 | 0.395 | 0.131 |
BF2 | 0.395 | 0.131 | 0.395 | |
BF3 | 0.691 | 0.395 | 0.395 | |
BF4 | 0.578 | 0.131 | 0.395 | |
S4 | BF1 | 0.395 | 0.131 | 0.113 |
BF2 | 0.395 | 0.131 | 0.131 | |
BF3 | 0.395 | 0.395 | 0.578 | |
BF4 | 0.395 | 0.395 | 0.395 | |
S5 | BF1 | 0.395 | 0.395 | 0.395 |
BF2 | 0.395 | 0.395 | 0.131 | |
BF3 | 0.395 | 0.395 | 0.578 | |
BF4 | 0.578 | 0.578 | 0.578 | |
S6 | BF1 | 0.395 | 0.578 | 0.578 |
BF2 | 0.578 | 0.578 | 0.578 | |
BF3 | 0.395 | 0.395 | 0.131 | |
BF4 | 0.395 | 0.578 | 0.395 | |
S7 | BF1 | 0.113 | 0.395 | 0.395 |
BF2 | 0.395 | 0.395 | 0.131 | |
BF3 | 0.113 | 0.131 | 0.131 | |
BF4 | 0.395 | 0.131 | 0.395 | |
S8 | BF1 | 0.578 | 0.578 | 0.113 |
BF2 | 0.691 | 0.578 | 0.395 | |
BF3 | 0.578 | 0.578 | 0.578 | |
BF4 | 0.578 | 0.578 | 0.578 | |
S9 | BF1 | 0.691 | 0.578 | 0.578 |
BF2 | 0.691 | 0.578 | 0.578 | |
BF3 | 0.691 | 0.578 | 0.578 | |
BF4 | 0.691 | 0.578 | 0.578 | |
S10 | BF1 | 0.395 | 0.113 | 0.131 |
BF2 | 0.395 | 0.395 | 0.395 | |
BF3 | 0.395 | 0.131 | 0.395 | |
BF4 | 0.395 | 0.131 | 0.395 |
Appendix B. Cloud Model Evaluation Process Data
Indicator | Ex1 | En1 | He1 |
---|---|---|---|
S1 | 0.5 | 0.0394 | 0.005 |
S2 | 0.691 | 0.0637 | 0.008 |
S3 | 0.691 | 0.0637 | 0.008 |
S4 | 0.5 | 0.0394 | 0.005 |
S5 | 0.691 | 0.0637 | 0.008 |
S6 | 0.5 | 0.0394 | 0.005 |
S7 | 0.5 | 0.0394 | 0.005 |
S8 | 0.691 | 0.0637 | 0.008 |
S9 | 1 | 0.1031 | 0.013 |
S10 | 0.5 | 0.0394 | 0.005 |
Indicator | Ex2 | En2 | He2 |
---|---|---|---|
S1 | 0.5 | 0.0394 | 0.005 |
S2 | 0.5 | 0.0394 | 0.005 |
S3 | 0.309 | 0.0637 | 0.008 |
S4 | 0.5 | 0.0394 | 0.005 |
S5 | 0.691 | 0.0637 | 0.008 |
S6 | 0.691 | 0.0637 | 0.008 |
S7 | 0.309 | 0.0637 | 0.008 |
S8 | 0.691 | 0.0637 | 0.008 |
S9 | 0.691 | 0.0637 | 0.008 |
S10 | 0.309 | 0.0637 | 0.008 |
Indicator | Ex3 | En3 | He3 |
---|---|---|---|
S1 | 0.5 | 0.0394 | 0.005 |
S2 | 0.5 | 0.0394 | 0.005 |
S3 | 0.5 | 0.0394 | 0.005 |
S4 | 0.5 | 0.0394 | 0.005 |
S5 | 0.691 | 0.0637 | 0.008 |
S6 | 0.5 | 0.0394 | 0.005 |
S7 | 0.5 | 0.0394 | 0.005 |
S8 | 0.691 | 0.0637 | 0.008 |
S9 | 0.691 | 0.0637 | 0.008 |
S10 | 0.5 | 0.0394 | 0.005 |
Appendix C. Expert Questionnaire
No. | Comparison | Which Is More Important? | Importance Level (1–9) |
---|---|---|---|
1 | Operating Cost vs. Air Quality | ||
2 | Operating Cost vs. Pressure | ||
3 | Operating Cost vs. Air Power | ||
4 | Operating Cost vs. Efficiency | ||
5 | Operating Cost vs. Productivity | ||
6 | Operating Cost vs. Safety | ||
7 | Operating Cost vs. Flexibility | ||
8 | Operating Cost vs. Noise | ||
9 | Operating Cost vs. Vibration | ||
10 | Air Quality vs. Pressure | ||
11 | Air Quality vs. Air Power | ||
12 | Air Quality vs. Efficiency | ||
13 | Air Quality vs. Productivity | ||
14 | Air Quality vs. Safety | ||
15 | Air Quality vs. Flexibility | ||
16 | Air Quality vs. Noise | ||
17 | Air Quality vs. Vibration | ||
18 | Pressure vs. Air Power | ||
19 | Pressure vs. Efficiency | ||
20 | Pressure vs. Productivity | ||
21 | Pressure vs. Safety | ||
22 | Pressure vs. Flexibility | ||
23 | Pressure vs. Noise | ||
24 | Pressure vs. Vibration | ||
25 | Air Power vs. Efficiency | ||
26 | Air Power vs. Productivity | ||
27 | Air Power vs. Safety | ||
28 | Air Power vs. Flexibility | ||
29 | Air Power vs. Noise | ||
30 | Air Power vs. Vibration | ||
31 | Efficiency vs. Productivity | ||
32 | Efficiency vs. Safety | ||
33 | Efficiency vs. Flexibility | ||
34 | Efficiency vs. Noise | ||
35 | Efficiency vs. Vibration | ||
36 | Productivity vs. Safety | ||
37 | Productivity vs. Flexibility | ||
38 | Productivity vs. Noise | ||
39 | Productivity vs. Vibration | ||
40 | Safety vs. Flexibility | ||
41 | Safety vs. Noise | ||
42 | Safety vs. Vibration | ||
43 | Flexibility vs. Noise | ||
44 | Flexibility vs. Vibration | ||
45 | Noise vs. Vibration |
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Scale | Relationship Between Two Factors |
---|---|
1 | Equal importance |
3 | Slightly more important |
5 | Clearly more important |
7 | Extremely more important |
9 | Absolutely more important |
2, 4, 6, 8 | Intermediate values between the above levels |
n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|
0 | 0 | 0.58 | 0.90 | 1.12 | 1.24 | 1.32 | 1.41 | 1.45 | 1.49 |
Superiority Language | Superiority Levels | Complex Spherical Fuzzy Parameters | Cloud Model Parameters |
---|---|---|---|
Excellent | I | ||
Good | II | ||
Average | III | ||
Below average | IV | ||
Poor | V |
Indicator | EW1 | EW2 | EW3 | CIW |
---|---|---|---|---|
S1 | 0.199 | 0.097 | 0.125 | 0.141 |
S2 | 0.072 | 0.170 | 0.125 | 0.120 |
S3 | 0.050 | 0.097 | 0.125 | 0.090 |
S4 | 0.072 | 0.170 | 0.125 | 0.120 |
S5 | 0.120 | 0.097 | 0.068 | 0.095 |
S6 | 0.120 | 0.026 | 0.030 | 0.060 |
S7 | 0.199 | 0.097 | 0.125 | 0.143 |
S8 | 0.031 | 0.038 | 0.125 | 0.066 |
S9 | 0.022 | 0.038 | 0.030 | 0.030 |
S10 | 0.115 | 0.170 | 0.125 | 0.135 |
Parameter | EW1 | EW2 | EW3 |
---|---|---|---|
CI | 0.022 | 0.010 | 0.003 |
RI | 1.49 | 1.49 | 1.49 |
10.198 | 10.093 | 10.023 | |
CR | 0.015 | 0.007 | 0.002 |
Level | I | II | III | IV | V |
---|---|---|---|---|---|
Score | 0.691 | 0.578 | 0.395 | 0.131 | 0.113 |
ES1 | ES2 | ES3 | ES | |
---|---|---|---|---|
BF1 | 0.35234 | 0.282734 | 0.228554 | 0.287876 |
BF2 | 0.397172 | 0.299204 | 0.279734 | 0.325370 |
BF3 | 0.402272 | 0.339176 | 0.398321 | 0.379923 |
BF4 | 0.471773 | 0.343781 | 0.429953 | 0.415169 |
Indicator | Ex | En | He |
---|---|---|---|
S1 | 0.5 | 0.0394 | 0.005 |
S2 | 0.56685 | 0.04791 | 0.00605 |
S3 | 0.5 | 0.05641 | 0.0071 |
S4 | 0.5 | 0.0394 | 0.005 |
S5 | 0.691 | 0.0637 | 0.008 |
S6 | 0.56685 | 0.04791 | 0.00605 |
S7 | 0.43315 | 0.04791 | 0.00605 |
S8 | 0.691 | 0.0637 | 0.008 |
S9 | 0.79915 | 0.07749 | 0.00975 |
S10 | 0.43315 | 0.04791 | 0.00605 |
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Yao, S.; Zhou, J.; Khandelwal, M.; Lawal, A.I.; Li, C.; Onifade, M.; Kwon, S. Intelligent Decision Framework for Booster Fan Optimization in Underground Coal Mines: Hybrid Spherical Fuzzy-Cloud Model Approach Enhancing Ventilation Safety and Operational Efficiency. Machines 2025, 13, 367. https://doi.org/10.3390/machines13050367
Yao S, Zhou J, Khandelwal M, Lawal AI, Li C, Onifade M, Kwon S. Intelligent Decision Framework for Booster Fan Optimization in Underground Coal Mines: Hybrid Spherical Fuzzy-Cloud Model Approach Enhancing Ventilation Safety and Operational Efficiency. Machines. 2025; 13(5):367. https://doi.org/10.3390/machines13050367
Chicago/Turabian StyleYao, Shibin, Jian Zhou, Manoj Khandelwal, Abiodun Ismail Lawal, Chuanqi Li, Moshood Onifade, and Sangki Kwon. 2025. "Intelligent Decision Framework for Booster Fan Optimization in Underground Coal Mines: Hybrid Spherical Fuzzy-Cloud Model Approach Enhancing Ventilation Safety and Operational Efficiency" Machines 13, no. 5: 367. https://doi.org/10.3390/machines13050367
APA StyleYao, S., Zhou, J., Khandelwal, M., Lawal, A. I., Li, C., Onifade, M., & Kwon, S. (2025). Intelligent Decision Framework for Booster Fan Optimization in Underground Coal Mines: Hybrid Spherical Fuzzy-Cloud Model Approach Enhancing Ventilation Safety and Operational Efficiency. Machines, 13(5), 367. https://doi.org/10.3390/machines13050367