Fuzzy Inductive Reasoning

1. Fuzzy Inductive Reasoning Predicting U.S. Food Demand in the 20th Century: A New Look at System Dynamics Mukund Moorthy, Graduate Student François E. Cellier, Professor Dept. of Electrical and Computer Engineering University of Arizona, Tucson, Arizona, U.S.A. Jeffrey T. LaFrance, Professor Dept. of Agricultural and Resource Economics University of California, Berkeley, U.S.A.

2. Contents • System Dynamics • Modeling Methodologies • Inductive Modeling Techniques • Fuzzy Inductive Reasoning • Plant and Signal Uncertainty • Modeling the Modeling Error • Food Demand Modeling • Conclusions

3. Levels and Rates Laundry List Levels Rates Inflows Outflows Population Birth Rate Death Rate Money Income Expenses Frustration Stress Affection Love Affection Frustration Tumor Cells Infection Treatment Inventory on Stock Shipments Sales Knowledge Learning Forgetting • Population • Material Standard of Living • Food Quality • Food Quantity • Education • Contraceptives • Religious Beliefs Birth Rate: System Dynamics

4. System Dynamics • Levels and Rates • Laundry List

5. Modeling Methodologies Knowledge-Based Approaches Pattern-Based Approaches Deep Models Shallow Models Inductive Reasoners Neural Networks FIR

6. Inductive Modeling Techniques • Making Models from Observations of Input/Output Behavior • Understanding Systems • Forecasting Systems Behavior • Controlling Systems Behavior

7. Comparisons • Deductive Modeling Techniques * have a large degree of validity in many different and even previously unknown applications * are often quite imprecise in their predictions due to inherent model inaccuracies • Inductive Modeling Techniques * have a limited degree of validity and can only be applied to predicting behavior of systems that are essentially known * are often amazingly precise in their predictions if applied carefully Ultimately, there exist only inductive models. Deductive modeling means using models that were previously derived by others --- in an inductive fashion.

8. More Comparisons Neural Networks Fuzzy Inductive R.

9. Fuzzy Inductive Reasoning • Discretization of quantitative information (Fuzzy Recoding) • Reasoning about discrete categories (Qualitative Modeling) • Inferring consequences about categories (Qualitative Simulation) • Interpolation between neighboring categories using fuzzy logic (Fuzzy Regeneration)

10. Quantitative Subsystem Quantitative Subsystem FIR Model FIR Model Recode Recode Regenerate Regenerate Fuzzy Inductive Reasoning Mixed Quantitative/Qualitative Modeling

11. Regenerate Regenerate Regenerate Regenerate Regenerate Application Cardiovascular System Central Nervous System Control (Qualitative Model) Hemodynamical System (Quantitative Model) Heart Rate Controller Heart Myocardiac ContractilityController Peripheric Resistance Controller Circulatory Flow Dynamics Venous Tone Controller Carotid Sinus Blood Pressure Coronary Resistance Controller Recode

12. Cardiovascular System Confidence Computation

13. Cardiovascular System Confidence Computation

14. Modeling the Error • Making predictions is easy! • Knowing how good the predictions are: That is the real problem! • A modeling/simulation methodology that doesn’t assess its own error is worthless! • Modeling the error can only be done in a statistical sense … because otherwise, the error could be subtracted from the prediction leading to a prediction without the error.

15. Fuzzification in FIR

16. Qualitative Simulation

17. Food Demand Modeling

18. Food Supply Food Demand Macroeconomy Population Dynamics Population Dynamics

19. Food Supply Food Demand Macroeconomy Population Dynamics Population Dynamics • Predicting Growth Functions k(n+1) = FIR [ k(n), P(n), k(n-1), P(n-1), … ]

20. 6 10 Food Supply Food Demand Macroeconomy Population Dynamics Population Dynamics %

21. Food Supply Food Demand Macroeconomy Population Dynamics Macroeconomy $ %

22. Food Supply Food Demand Macroeconomy Population Dynamics Macroeconomy % %

23. Food Supply Food Demand Macroeconomy Population Dynamics Food Demand/Supply £ %

24. Applications • Cardiovascular System Modeling for Classification of Anomalies • Anaesthesiology Model for Control of Depth of Anaesthesia During Surgery • Shrimp Growth Model for El Remolino Shrimp Farm in Northern México • Prediction of Water Demand in Barcelona and Rotterdam • Design of Fuzzy Controller for Tanker Ship Steering • Fault Diagnosis on Nuclear Power Plants • Prediction of Technology Changes in the Telecommunication Sector

25. Dissertations • Àngela Nebot (1994) Qualitative Modeling and Simulation of Biomedical Systems Using Fuzzy Inductive Reasoning • Francisco Mugica (1995) Diseño Sistemático de Controladores Difusos Usando Razonamiento Inductivo • Álvaro de Albornoz (1996) Inductive Reasoning and Reconstruction Analysis: Two Complementary Tools for Qualitative Fault Monitoring of Large-Scale Systems • Josefina López (1998) Qualitative Modeling and Simulation of Time Series Using Fuzzy Inductive Reasoning • Sebastián Medina (1998) Knowledge Generalization from Observation

26. Primary Publications • F.E.Cellier (1991) Continuous System Modeling, Springer-Verlag, New York. • F.E.Cellier, A.Nebot, F. Mugica, and A. de Albornoz (1996) Combined Qualitative/Quantitative Simulation Models of Continuous-Time Processes Using Fuzzy Inductive Reasoning Techniques, Intl. J. General Systems. • A. Nebot, F.E. Cellier, and M. Vallverdú (1998) Mixed Quantitative/Qualitative Modeling and Simulation of the Cardiovascular System, Comp. Programs in Biomedicine. • International Journal of General Systems (1998) Special Issue on Fuzzy Inductive Reasoning. • http://www.ece.arizona.edu/~cellier/publications_fir.html Web site about FIR publications.

27. Conclusions • Fuzzy Inductive Reasoning offers an exciting alternative to Neural Networks for modeling systems from observations of behavior. • Fuzzy Inductive Reasoning is highly robust when used correctly. • Fuzzy Inductive Reasoning features a model synthesis capability rather than a model learning approach. It is therefore quite fast in setting up the model. • Fuzzy Inductive Reasoning offers a self-assessment feature, which is easily the most important characteristic of the methodology. • Fuzzy Inductive Reasoning is a practical tool with many industrial applications. Contrary to most other qualitative modeling techniques, FIR doesn´t suffer from scale-up problems.