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

2. Jump to first page Contents n System Dynamics n Modeling Methodologies n Inductive Modeling Techniques n Fuzzy Inductive Reasoning n Plant and Signal Uncertainty n Modeling the Modeling Error n Food Demand Modeling n Conclusions

3. Jump to first page System Dynamics n Levels and Rates n Laundry List Levels Rates Inflows Outflows PopulationBirth RateDeath Rate MoneyIncomeExpenses FrustrationStressAffection LoveAffectionFrustration Tumor CellsInfectionTreatment Inventory on StockShipmentsSales KnowledgeLearningForgetting Birth Rate: Population Material Standard of Living Food Quality Food Quantity Education Contraceptives Religious Beliefs

4. Jump to first page System Dynamics n Levels and Rates n Laundry List

5. Jump to first page Modeling Methodologies Knowledge-Based Approaches Pattern-Based Approaches Deep ModelsShallow Models Neural NetworksInductive Reasoners FIR

6. Jump to first page Inductive Modeling Techniques n Making Models from Observations of Input/Output Behavior n Understanding Systems n Forecasting Systems Behavior n Controlling Systems Behavior

7. Jump to first page Comparisons n 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 n 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. Jump to first page More Comparisons Neural NetworksFuzzy Inductive R.

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

10. Jump to first page Fuzzy Inductive Reasoning Mixed Quantitative/Qualitative Modeling Quantitative Subsystem Recode FIR Model Regenerate Quantitative Subsystem Recode FIR Model Regenerate

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

12. Jump to first page Cardiovascular System Confidence Computation

13. Jump to first page Cardiovascular System Confidence Computation

14. Jump to first page Modeling the Error n Making predictions is easy! n Knowing how good the predictions are: That is the real problem! n A modeling/simulation methodology that doesn’t assess its own error is worthless! n 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. Jump to first page Fuzzification in FIR

16. Jump to first page Qualitative Simulation

17. Jump to first page Food Demand Modeling

18. Jump to first page Population Dynamics Macroeconomy Food Demand Food Supply

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

20. Jump to first page Population Dynamics Macroeconomy Food Demand Food Supply 10 6 %

21. Jump to first page Macroeconomy Population Dynamics Macroeconomy Food Demand Food Supply $ %

22. Jump to first page Macroeconomy Population Dynamics Macroeconomy Food Demand Food Supply % %

23. Jump to first page Food Demand/Supply Population Dynamics Macroeconomy Food Demand Food Supply £ %

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

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

26. Jump to first page Primary Publications n F.E.Cellier (1991) Continuous System Modeling, Springer- Verlag, New York. n 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. n A. Nebot, F.E. Cellier, and M. Vallverdú (1998) Mixed Quantitative/Qualitative Modeling and Simulation of the Cardiovascular System, Comp. Programs in Biomedicine. n International Journal of General Systems (1998) Special Issue on Fuzzy Inductive Reasoning. n http://www.ece.arizona.edu/~cellier/publications_fir.html Web site about FIR publications.

27. Jump to first page Conclusions n Fuzzy Inductive Reasoning offers an exciting alternative to Neural Networks for modeling systems from observations of behavior. n Fuzzy Inductive Reasoning is highly robust when used correctly. n Fuzzy Inductive Reasoning features a model synthesis capability rather than a model learning approach. It is therefore quite fast in setting up the model. n Fuzzy Inductive Reasoning offers a self-assessment feature, which is easily the most important characteristic of the methodology. n 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.