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TS Modeling Based on GMDH and Its application

TS Modeling Based on GMDH and Its application. Changzheng He Dept. of Management Science, Sichuan University of P.R.China. Fuzzy modeling. ☆ Two main type in fuzzy modeling —— Mamdani Type —— TS Type. FRI. Mamdani Type fuzzy model. ＝. ＋. GMDH.

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TS Modeling Based on GMDH and Its application

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

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

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

  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. TS fuzzy model 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

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

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

  11. Steps of algorithm （1） Fuzzification of variables and data division Training set Test set Validation set A B N

  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 Parametersare estimated by Ordinary LeastSquarein the training set A.

  15. Steps of algorithm （3） Model selection Fbest 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 Fbest 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 External Criterion stop

  19. Network of TS-GMDHmodeling

  20. Simulation Experiment 12 benchmark data sets from UCI

  21. Experiment Results

  22. Simulation Experiment Conclusion: ☆ 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

  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 TS-GMDH have a better accuracy in both modeling set M and validation set N

  25. Q & A

  26. Thank You !

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