1. TS Modeling Based on GMDH and Its application Changzheng He Dept. of Management Science, Sichuan University of P.R.China

2. Fuzzy modeling ☆ Two main type in fuzzy modeling —— Mamdani Type —— TS Type

3. Self-organizing Fuzzy Rule Induction GMDH Mamdani Type fuzzy model FRI ＋＝

4. 1 w 1 v 2 v 3 v 2 w 4 v 5 v 10 w 2 z 2 y )( * vfy  w 5 Z 6 Initial organisaction 1. layer 2. layer 3. layer best models not selected neuron selected neuron GMDH algorithm

5. Self-organizing Fuzzy Rule Induction J.A.Muellerj F. Lemke fuzzification

6. FRI in marketing ☆ Extract features from data automatically ☆ Form fuzzy models similar to natural language

7. TS model Takagi-Sugeno fuzzy model ☆ Proposed by Japanese researcher Takagi and Sugeno in 1985. ☆ Widely used in control 、 prediction

8. Basic form of TS model ☆ Consist of several If-then rules, each rule is as following: Where and are input\output variables are fuzzy set defined in input variable TS fuzzy model

9. Advantage of TS model ☆ Approximates complex nonlinear systems with fewer rules and high modeling accuracy

10. TS-GMDH GMDH TS Type fuzzy model TS-GMDH ＋＝

11. Steps of algorithm （ 1 ） Fuzzification of variables and data division Test setValidation setTraining set ABN

12. Steps of algorithm Bell-shaped membership functions are used

13. Steps of algorithm （ 2 ） Forming of the first generation TS models. Input fuzzy sets are combined in pairs to form the first generation TS models ……

14. Steps of algorithm In the TS fuzzy rule Parameters are estimated by Ordinary Least Square in the training set A.

15. Steps of algorithm （ 3 ） Model selection F best TS models are selected in the test set B by Regularity criterion where and are firing strength of each rule, and are predicted output of each rule

16. Steps of algorithm （ 4 ） Rules fusion F best TS model are merged into F rules

17. Steps of algorithm （ 5 ） Forming the 2th generation TS models F best rule are combined in pairs to form models

18. Steps of algorithm （ 6 ） Circulation of algorithm Model generation Model selection Rule Fusion External Criterion stop

19. Network of TS-GMDH modeling

20. Simulation Experiment 12 benchmark data sets from UCI Number of sample Number of attribute Credit 100020 Pima 7688 Haberman 3063 Endgame 9589 Echocardiogram 13212 Hepatitis 15519 MAGIC 1902010 monks-1.train 4327 monks-1.test 4327 Mass 9615 Breast Cancer_D 56931 Breast Cancer_P 19833

21. Experiment Results FRITS-GMDH Credit 70.18%72.42% Pima 71.33%75.30% Haberman 52.58%73.53% Endgame 67.64%69.13% Echocardiogram 87.27%96.12% Hepatitis 84.50%84.52% MAGIC 67.79%79.38% monks-1.train 74.42%80.08% monks-1.test 74.36%80.57% Mass 79.58%81.76% Breast Cancer_D 90.56%94.48% Breast Cancer_P 76.24%75.19%

22. Simulation Experiment ☆ TS-GMDH have better accuracy in 11of 12 data set; ☆ In the exceptional case it is not statistically significant which means TS-GMDH in not worse than FRI Conclusion:

23. Empirical research Feature extraction of cigarette market Problem description Draw features of two segments: heavy smokers and mild smokers Data size: 150 sample and 50 variables

24. Empirical research Method Heavy SmokerMild Smoker NM(A+B)N FRI 83.33%70%83.33%70% TS-GMDH 94%93.33%89.33%87.33% TS-GMDH have a better accuracy in both modeling set M and validation set N