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Designing Antecedent Membership Functions

Designing Antecedent Membership Functions. Recommend designer to adopt the following design principles: Each Membership function overlaps only with the closest neighboring membership functions;

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Designing Antecedent Membership Functions

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  1. Designing Antecedent Membership Functions • Recommend designer to adopt the following design principles: • Each Membership function overlaps only with the closest neighboring membership functions; • For any possible input data, its membership values in all relevant fuzzy sets should sum to 1 (or nearly) * Fuzzy Logic: Intelligence, control, and Information, J. Yen and R. Langari, Prentice Hall

  2. Designing Antecedent Membership Functions A Membership Function Design that violates the second principle * Fuzzy Logic: Intelligence, control, and Information, J. Yen and R. Langari, Prentice Hall

  3. Designing Antecedent Membership Functions A Membership Function Design that violates both principle * Fuzzy Logic: Intelligence, control, and Information, J. Yen and R. Langari, Prentice Hall

  4. Designing Antecedent Membership Functions A symmetric Function Design Following the guidelines * Fuzzy Logic: Intelligence, control, and Information, J. Yen and R. Langari, Prentice Hall

  5. Designing Antecedent Membership Functions An asymmetric Function Design Following the guidelines * Fuzzy Logic: Intelligence, control, and Information, J. Yen and R. Langari, Prentice Hall

  6. Example: Furnace Temperature Control • Inputs • Temperature reading from sensor • Furnace Setting • Output • Power control to motor * Fuzzy Systems Toolbox, M. Beale and H Demuth

  7. MATLAB: Create membership functions - Temp * Fuzzy Systems Toolbox, M. Beale and H Demuth

  8. MATLAB: Create membership functions - Setting * Fuzzy Systems Toolbox, M. Beale and H Demuth

  9. MATLAB: Create membership functions - Power * Fuzzy Systems Toolbox, M. Beale and H Demuth

  10. If - then - Rules * Fuzzy Systems Toolbox, M. Beale and H Demuth

  11. Antecedent Table * Fuzzy Systems Toolbox, M. Beale and H Demuth

  12. Antecedent Table • MATLAB • A = table(1:5,1:3); • Table generates matrix represents a table of all possible combinations * Fuzzy Systems Toolbox, M. Beale and H Demuth

  13. Consequence Matrix * Fuzzy Systems Toolbox, M. Beale and H Demuth

  14. Evaluating Rules with Function FRULE * Fuzzy Systems Toolbox, M. Beale and H Demuth

  15. Design Guideline (Inference) • Recommend • Max-Min (Clipping) Inference method be used together with the MAX aggregation operator and the MIN AND method • Max-Product (Scaling) Inference method be used together with the SUM aggregation operator and the PRODUCT AND method * Fuzzy Logic: Intelligence, control, and Information, J. Yen and R. Langari, Prentice Hall

  16. Example: Fully Automatic Washing Machine * Fuzzy Logic: Intelligence, control, and Information, J. Yen and R. Langari, Prentice Hall

  17. Example: Fully Automatic Washing Machine • Inputs • Laundry Softness • Laundry Quantity • Outputs • Washing Cycle • Washing Time * Fuzzy Logic: Intelligence, control, and Information, J. Yen and R. Langari, Prentice Hall

  18. Example: Input Membership functions * Fuzzy Logic: Intelligence, control, and Information, J. Yen and R. Langari, Prentice Hall

  19. Example: Output Membership functions * Fuzzy Logic: Intelligence, control, and Information, J. Yen and R. Langari, Prentice Hall

  20. Example: Fuzzy Rules for Washing Cycle * Fuzzy Logic: Intelligence, control, and Information, J. Yen and R. Langari, Prentice Hall

  21. Example: Control Surface View (Clipping) * Fuzzy Logic: Intelligence, control, and Information, J. Yen and R. Langari, Prentice Hall

  22. Example: Control Surface View (Scaling) * Fuzzy Logic: Intelligence, control, and Information, J. Yen and R. Langari, Prentice Hall

  23. Example: Control Surface View Scaling Clipping * Fuzzy Logic: Intelligence, control, and Information, J. Yen and R. Langari, Prentice Hall

  24. Example: Rule View (Clipping) * Fuzzy Logic: Intelligence, control, and Information, J. Yen and R. Langari, Prentice Hall

  25. Example: Rule View (Scaling) * Fuzzy Logic: Intelligence, control, and Information, J. Yen and R. Langari, Prentice Hall

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