Neuro-fuzzy Approach - Computational Intelligence in Time Series Forecasting - page 251

Table 6.2(b). Comparison of training and prediction performance of fuzzy and other model
with selected Takagi-Sugeno-type multi-input single-output neuro-fuzzy network with
proposed Levenberg-Marquardt training algorithm for Mackey-Glass chaotic time series.

Sl. No. Method Training /

forecasting with
Input data

RMSE
prediction error

1. Kim and Kim

(coarse partition)

500 0.050809 (5 partitions)

0.044957 (7 partitions)
0.038011 (9 partitions)

2. Kim and Kim

(after fine tuning)

500 0.049206 (5 partitions)

0.042275 (7 partitions)
0.037873 (9 partitions)

3. Kim and Kim

(genetic-fuzzy predictor
ensemble)

500 0.026431

4. Lee and Kim 500 0.0816

5. Wang (product operator) 500 0.0907

6. Min operator 500 0.0904

7. Jang (ANFIS) 500 0.0070 (16 rules)

8. Auto regression model 500 0.19

9. Cascade correlation neural

network

500 0.06

10. Backpropagation neural

network

500 0.02

11. Sixth-order polynomial 500 0.04

12. Linear prediction model 500 0.55

13. FPNN (quadratic polynomial

fuzzy inference)

500 0.0012 (16 rules)

14. Takagi-Sugeno-type multi-

input single-output neuro-
fuzzy network (proposed
work)

500 (forecasting) 0.0053 (7 rules,

7 GMFs,
non-optimized)

N

2

RMSE = , e r is the error due to r th training sample and N is the number ¦ e N

r

r 1

of training / predicted data samples.