Research Article
A Method Based on Extended Fuzzy Transforms to Approximate Fuzzy Numbers in Mamdani Fuzzy Rule-Based System
(a) Parameters and RMSE of the approximation for fuzzy sets of x1 |
| x1 (m2) | Fuzzy number | a | c | d | b | RMSE |
| Low | 20 | 20 | 45 | 70 | 9.11×10-3 | Mean Low | 45 | 70 | 75 | 90 | 9.91×10-3 | Mean | 75 | 90 | 95 | 100 | 9.17×10-3 | Mean High | 95 | 100 | 115 | 125 | 9.76×10-3 | High | 110 | 120 | 150 | 150 | 9.34×10-3 |
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(b) Parameters and RMSE of the approximation for fuzzy sets of x2 |
| x2 | Fuzzy number | a | c | d | b | RMSE |
| Low | 0 | 0 | 1 | 4 | 9.18×10-3 | Mean Low | 0.5 | 3 | 6 | 8 | 9.43×10-3 | Mean | 2 | 7 | 12 | 20 | 9.19×10-3 | Mean High | 8 | 12 | 15 | 25 | 9.57×10-3 | High | 15 | 25 | 50 | 50 | 9.15×10-3 |
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(c) Parameters and RMSE of the approximation for fuzzy sets of x3 |
| x3 | Fuzzy number | a | c | d | b | RMSE |
| Low | 0 | 0 | 0.5 | 1 | 9.21×10-3 | Mean Low | 0.4 | 0.6 | 1 | 1.5 | 9.35×10-3 | Mean | 1 | 2 | 4 | 6 | 9.33×10-3 | Mean High | 2 | 4 | 7 | 10 | 9.02×10-3 | High | 6 | 10 | 30 | 30 | 9.26×10-3 |
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(d) Parameters and RMSE of the approximation for fuzzy sets of x4 |
| x4 | Fuzzy number | a | c | d | b | RMSE |
| Low | 0 | 0 | 30 | 40 | 9.24×10-3 | Mean Low | 30 | 50 | 60 | 70 | 9.29×10-3 | Mean | 60 | 65 | 70 | 80 | 9.49×10-3 | Mean High | 75 | 80 | 85 | 90 | 9.35×10-3 | High | 85 | 95 | 100 | 100 | 9.08×10-3 |
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(e) Parameters and RMSE of the approximation for fuzzy sets of x5 |
| x5 | Fuzzy number | a | c | d | b | RMSE |
| Low | 0 | 0 | 10 | 15 | 9.30×10-3 | Mean Low | 7 | 15 | 20 | 25 | 9.52×10-3 | Mean | 20 | 25 | 30 | 35 | 9.25×10-3 | Mean High | 30 | 35 | 40 | 50 | 9.31×10-3 | High | 40 | 50 | 100 | 100 | 9.37×10-3 |
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(f) Parameters and RMSE of the approximation for fuzzy sets of x6 |
| x6 | Fuzzy number | a | c | d | b | RMSE |
| Low | 0 | 0 | 10 | 15 | 9.32×10-3 | Mean Low | 7 | 15 | 25 | 30 | 9.19×10-3 | Mean | 22 | 28 | 32 | 35 | 9.24×10-3 | Mean High | 30 | 40 | 45 | 55 | 9.48×10-3 | High | 50 | 60 | 100 | 100 | 9.28×10-3 |
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