Application of a Similarity Measure Using Fuzzy Sets to Select the Optimal Plan for an Air-Assisted Rice Seeder
Abstract
:1. Introduction
2. Materials and Methods
2.1. Sowing Machine Problem
2.2. Fuzzy Sets and Similarity Measures
- +
- Subset: if for all ,
- +
- Equal: if for all ,
- +
- Intersection: ,
- +
- Union: ,
- +
- Complement: ,
- +
- For all real numbers .
- (S1)
- for all ,
- (S2)
- for all ,
- (S3)
- if for all ,
- (S4)
- For all , , , if , then .
2.2.1. New Similarity Measure for Fuzzy Sets
2.2.2. Comparison to Other Similarity Measures for Fuzzy Sets
Algorithm 1 Solving pattern recognition problems using similarity measures. |
Step 1. Calculate all similarity measures from sample to patterns for all . Step 2. Classify sample into pattern with . |
2.3. Fuzzy Similarity-Based MCDM
Algorithm 2 The fuzzy similarity-based TOPSIS model |
Step 1: Normalize the data table according to each criterion to obtain a fuzzy decision matrix. Step 2: Determine weight of each criterion. Step 3: Define the best option and worst option . Step 4: Use Equation (2) to compute the similarity measures and for each alternative to identify and , respectively. Step 5. Determine the close coefficient , whereby can be considered the decision set of alternatives. Step 6. Rank if for all |
2.4. Correlation Coefficient
3. Results
- +
- Air-assisted velocity
- +
- Internal diameter of injection port
- +
- Distant between injection port and soil surface
- +
- Seeding area precision (diameter 50 mm)
- +
- Seeding area precision (diameter 100 mm)
- +
- Seeding area precision (diameter 150 mm)
- +
- Seeding depth
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
C1 | C2 | C3 | C4 | C5 | C6 | |
---|---|---|---|---|---|---|
E1 | 0.5 | 0 | 1.00 | 1.00 | 1.00 | 0 |
E2 | 0.5 | 0.375 | 1.00 | 0.97 | 1.00 | 0 |
E3 | 0.5 | 1 | 1.00 | 0.81 | 1.00 | 0.6 |
E4 | 0.5 | 1 | 0.75 | 0.77 | 0.98 | 1 |
E5 | 0.5 | 0 | 0.00 | 0.60 | 0.92 | 0 |
E6 | 1 | 0 | 1.00 | 0.99 | 1.00 | 0 |
E7 | 1 | 0.375 | 1.00 | 0.91 | 1.00 | 0.6 |
E8 | 1 | 1 | 0.95 | 0.79 | 1.00 | 1 |
E9 | 1 | 1 | 0.50 | 0.74 | 0.96 | 0 |
E10 | 1 | 0 | 0.00 | 0.55 | 0.88 | 0 |
E11 | 0.3333 | 0 | 1.00 | 0.81 | 1.00 | 0 |
E12 | 0.3333 | 0.375 | 0.60 | 0.78 | 0.94 | 1 |
E13 | 0.3333 | 1 | 0.00 | 0.73 | 0.85 | 0 |
E14 | 0.3333 | 1 | 0.00 | 0.65 | 0.79 | 0 |
E15 | 0.3333 | 0 | 0.00 | 0.57 | 0.71 | 0 |
E16 | 0.5 | 0 | 1.00 | 0.98 | 1.00 | 0 |
E17 | 0.5 | 0.375 | 1.00 | 0.92 | 1.00 | 0 |
E18 | 0.5 | 1 | 1.00 | 0.81 | 1.00 | 0.6 |
E19 | 0.5 | 1 | 0.65 | 0.78 | 0.95 | 1 |
E20 | 0.5 | 0 | 0.00 | 0.56 | 0.88 | 0 |
E21 | 0.3333 | 0 | 1.00 | 0.97 | 1.00 | 0 |
E22 | 0.3333 | 0.375 | 1.00 | 0.89 | 1.00 | 0.8 |
E23 | 0.3333 | 1 | 0.80 | 0.80 | 0.96 | 0 |
E24 | 0.3333 | 1 | 0.35 | 0.73 | 0.94 | 0 |
E25 | 0.3333 | 0 | 0.00 | 0.54 | 0.87 | 0 |
P− | 0.3333 | 0 | 0 | 0.54 | 0.71 | 0 |
P+ | 1 | 1 | 1 | 1 | 1 | 1 |
Appendix B
S+ | S− | CC | |
---|---|---|---|
E1 | 0.4333 | 0.672 | 0.392 |
E2 | 0.4599 | 0.6617 | 0.41 |
E3 | 0.8531 | 0.4149 | 0.6728 |
E4 | 0.9335 | 0.2512 | 0.788 |
E5 | 0.1188 | 0.988 | 0.1073 |
E6 | 0.4498 | 0.652 | 0.4082 |
E7 | 0.8499 | 0.4293 | 0.6644 |
E8 | 0.9865 | 0.1379 | 0.8774 |
E9 | 0.3915 | 0.8123 | 0.3252 |
E10 | 0.1323 | 0.9701 | 0.12 |
E11 | 0.4198 | 0.6837 | 0.3804 |
E12 | 0.8696 | 0.3466 | 0.715 |
E13 | 0.1631 | 0.941 | 0.1477 |
E14 | 0.1585 | 0.945 | 0.1436 |
E15 | 0.1028 | 0.9992 | 0.0933 |
E16 | 0.4328 | 0.6729 | 0.3914 |
E17 | 0.4585 | 0.6637 | 0.4086 |
E18 | 0.8531 | 0.4149 | 0.6728 |
E19 | 0.9122 | 0.2874 | 0.7604 |
E20 | 0.116 | 0.9903 | 0.1049 |
E21 | 0.4242 | 0.6778 | 0.3849 |
E22 | 0.8938 | 0.336 | 0.7268 |
E23 | 0.4351 | 0.7354 | 0.3717 |
E24 | 0.3212 | 0.8746 | 0.2686 |
E25 | 0.1066 | 1 | 0.0963 |
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C1 | C2 | C3 | C4 | C5 | C6 | C7 | |
---|---|---|---|---|---|---|---|
E1 | 6 | 12 | 50 | 100 | 0 | 0 | 26 |
E2 | 6 | 12 | 100 | 97 | 3 | 0 | 17 |
E3 | 6 | 12 | 150 | 81 | 19 | 0 | 12 |
E4 | 6 | 12 | 200 | 75 | 23 | 2 | 6 |
E5 | 6 | 12 | 250 | 52 | 40 | 8 | 3 |
E6 | 5 | 15 | 50 | 99 | 1 | 0 | 20 |
E7 | 5 | 15 | 100 | 91 | 9 | 0 | 12 |
E8 | 5 | 15 | 150 | 79 | 21 | 0 | 6 |
E9 | 5 | 15 | 200 | 70 | 28 | 4 | 3 |
E10 | 5 | 15 | 250 | 43 | 45 | 12 | 1 |
E11 | 4 | 18 | 50 | 81 | 19 | 0 | 16 |
E12 | 4 | 18 | 100 | 72 | 22 | 6 | 7 |
E13 | 4 | 18 | 150 | 58 | 28 | 15 | 3 |
E14 | 4 | 18 | 200 | 44 | 35 | 21 | 2 |
E15 | 4 | 18 | 250 | 28 | 43 | 29 | 1 |
E16 | 6 | 15 | 50 | 98 | 2 | 0 | 25 |
E17 | 6 | 15 | 100 | 92 | 8 | 0 | 15 |
E18 | 6 | 15 | 150 | 81 | 19 | 0 | 12 |
E19 | 6 | 15 | 200 | 73 | 22 | 5 | 5 |
E20 | 6 | 15 | 250 | 44 | 44 | 12 | 2 |
E21 | 4 | 15 | 50 | 97 | 3 | 0 | 15 |
E22 | 4 | 15 | 100 | 89 | 11 | 0 | 11 |
E23 | 4 | 15 | 150 | 76 | 4 | 0 | 3 |
E24 | 4 | 15 | 200 | 67 | 27 | 6 | 2 |
E25 | 4 | 15 | 250 | 41 | 46 | 13 | 1 |
Similarity Measures | The Similarity Measures for Classifying Sample B in Patterns Ai | Classification Results | ||
---|---|---|---|---|
Equation (3) | 0.9150 | 0.9138 | 0.9350 | |
Equation (4) | 0.6000 | 0.6000 | 0.7000 | |
Equation (5) | 0.8148 | 0.8136 | 0.8485 | |
Equation (6) | 0.8750 | 0.8625 | 0.8750 | Null |
Equation (7) | 0.4054 | 0.4865 | 0.3333 | |
Equation (8) | 0.6875 | 0.6857 | 0.7368 | |
Equation (9) | 0.8333 | 1 | 0.8333 | |
Equation (10) | 0.6486 | 0.6967 | 0.7158 | |
Equation (11) | 0.7583 | 0.6875 | 0.7667 | |
Equation (12) | 0.9318 | 0.9285 | 0.9414 | |
Equation (13) | 0.5000 | 0.6000 | 0.5000 | |
Equation (14) | 0.6875 | 0.7500 | 0.8235 | |
Equation (15) | 1 | 0.8889 | 0.8235 | |
Equation (16) | 0.6875 | 0.7500 | 0.8750 | |
Equation (17) | 0.6875 | 0.7500 | 0.8235 | |
Equation (2) (proposed measure) | 0.9243 | 0.9179 | 0.9281 |
Similarity Measures | The Similarity Measures for Classifying Sample B in Patterns Ai | Classification Results | ||
---|---|---|---|---|
Equation (3) | 0.6100 | 0.8000 | 0.7727 | |
Equation (4) | 0.3000 | 0.6000 | 0.5000 | |
Equation (5) | 0.5789 | 0.8000 | 0.7727 | |
Equation (6) | 0.6000 | 0.7750 | 0.7500 | |
Equation (7) | 0.2308 | 0.2308 | 0.2051 | Null |
Equation (8) | 0.4074 | 0.6667 | 0.6296 | |
Equation (9) | 0.5556 | 0.5556 | 0.5556 | Null |
Equation (10) | 0.4000 | 0.5902 | 0.5630 | |
Equation (11) | 0.4201 | 0.7138 | 0.6674 | |
Equation (12) | 0.6930 | 0.8590 | 0.8380 | |
Equation (13) | 0.5000 | 0.5000 | 0.5000 | Null |
Equation (14) | 0.4074 | 0.6667 | 0.6296 | |
Equation (15) | 1 | 1 | 1 | Null |
Equation (16) | 0.4074 | 0.6667 | 0.6296 | |
Equation (17) | 0.4074 | 0.6667 | 0.6296 | |
Equation (9) (proposed measure) | 0.731 | 0.8618 | 0.8448 |
Selections | 1st | 2nd | 3rd | 4th | 5th |
---|---|---|---|---|---|
Air-assisted velocity (m/s) | 5 | 6 | 6 | 4 | 4 |
Distant between injection port and soil surface (mm) | 150 | 200 | 200 | 100 | 100 |
Diameter of injection port (mm) | 15 | 12 | 15 | 18 | 15 |
Seeding area precision, diameter 50 mm (%) | 79 | 75 | 73 | 72 | 89 |
Seeding area precision, diameter 100 mm (%) | 21 | 23 | 22 | 22 | 11 |
Seeding area precision, diameter 150 mm (%) | 0 | 2 | 5 | 6 | 0 |
Seeding depth (mm) | 6 | 6 | 5 | 7 | 11 |
Weight Vectors | The Top Three Ranking | Meaning | Correlation Coefficients |
---|---|---|---|
w1 = (0.025, 0.025, 0.025, 0.2, 0.1, 0.025, 0.6) | Good | hstq1 | |
w2 = (0.05, 0.05, 0.05, 0.2, 0.1, 0.05, 0.5) | Good | hstq2 | |
w3 = (0.05, 0.05, 0.05, 0.2, 0.05, 0.05, 0.55) | Good | hstq2 | |
w4 = (0.05, 0.05, 0.05, 0.2, 0.1, 0.5, 0.05) | Bad | hstq4 | |
w5 = (0.05, 0.05, 0.05, 0.5, 0.1, 0.05, 0.2) | Bad | hstq5 | |
w6 = (0.05, 0.05, 0.15, 0.25, 0.05, 0.05, 0.4) | Pretty good | hstq6 |
hstq1 | hstq2 | hstq3 | hstq 4 | hstq 5 | hstq 6 | |
---|---|---|---|---|---|---|
C1 | 0.1757 | 0.2044 | 0.1994 | 0.2786 | 0.2178 | 0.1988 |
C2 | 0.0906 | 0.1265 | 0.1183 | 0.2671 | 0.2017 | 0.1389 |
C3 | 0.427 | 0.4526 | 0.4583 | 0.2887 | 0.2563 | 0.567 |
C4 | 0.6191 | 0.6522 | 0.6214 | 0.9532 | 0.954 | 0.6837 |
C5 | 0.4018 | 0.4373 | 0.4014 | 0.8214 | 0.8019 | 0.4765 |
C6 | 0.5628 | 0.597 | 0.57 | 0.8945 | 0.853 | 0.6241 |
C7 | 0.9455 | 0.9252 | 0.9398 | 0.5056 | 0.5859 | 0.8735 |
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Hai, N.T.; Chosa, T.; Tojo, S.; Thi-Hien, N. Application of a Similarity Measure Using Fuzzy Sets to Select the Optimal Plan for an Air-Assisted Rice Seeder. Appl. Sci. 2021, 11, 6715. https://doi.org/10.3390/app11156715
Hai NT, Chosa T, Tojo S, Thi-Hien N. Application of a Similarity Measure Using Fuzzy Sets to Select the Optimal Plan for an Air-Assisted Rice Seeder. Applied Sciences. 2021; 11(15):6715. https://doi.org/10.3390/app11156715
Chicago/Turabian StyleHai, Nguyen Thanh, Tadashi Chosa, Seishu Tojo, and Ngo Thi-Hien. 2021. "Application of a Similarity Measure Using Fuzzy Sets to Select the Optimal Plan for an Air-Assisted Rice Seeder" Applied Sciences 11, no. 15: 6715. https://doi.org/10.3390/app11156715
APA StyleHai, N. T., Chosa, T., Tojo, S., & Thi-Hien, N. (2021). Application of a Similarity Measure Using Fuzzy Sets to Select the Optimal Plan for an Air-Assisted Rice Seeder. Applied Sciences, 11(15), 6715. https://doi.org/10.3390/app11156715