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Fuzzy Inductive ReasoningPredicting 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.
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Contents System Dynamics Modeling Methodologies Inductive Modeling Techniques Fuzzy Inductive Reasoning Plant and Signal Uncertainty Modeling the Modeling Error Food Demand Modeling Conclusions
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System Dynamics Levels and Rates
Laundry List
Levels Rates Inflows Outflows
Population Birth Rate Death RateMoney Income ExpensesFrustration Stress AffectionLove Affection FrustrationTumor Cells Infection TreatmentInventory on Stock Shipments SalesKnowledge Learning Forgetting
Birth Rate:
• Population• Material Standard of Living• Food Quality• Food Quantity• Education• Contraceptives• Religious Beliefs
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Modeling Methodologies
Knowledge-BasedApproaches
Pattern-BasedApproaches
Deep Models Shallow Models
Neural NetworksInductive Reasoners
FIR
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Inductive Modeling Techniques
Making Models from Observations of Input/Output Behavior
Understanding Systems
Forecasting Systems Behavior
Controlling Systems Behavior
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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.
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More Comparisons
Quantitative Qualitative
Parametric Non-parametric
Adaptive Limited Adaptability
Slow Training Fast Setup
Smooth Interpolation Decent Interpolation
Wild Extrapolation No Extrapolation
No Error Estimate Error Estimate
Unsafe / Gullible Robust / Self-critical
Neural Networks Fuzzy Inductive R.
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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)
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Fuzzy Inductive ReasoningMixed Quantitative/Qualitative Modeling
Quantitative Subsystem
Recode FIR Model
Regenerate
Quantitative Subsystem
Recode
FIR Model
Regenerate
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ApplicationCardiovascular System
Heart Rate Controller
Myocardiac Contractility Controller
Peripheric Resistance Controller
Venous Tone Controller
Coronary Resistance Controller
Central Nervous System Control (Qualitative Model)
Regenerate
Regenerate
Regenerate
Regenerate
Regenerate
Heart
Circulatory Flow
Dynamics
Carotid Sinus Blood Pressure
Recode
Hemodynamical System (Quantitative Model)
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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.
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Population Dynamics Predicting Growth Functions
Population Dynamics
Macroeconomy
Food Demand
Food Supplyk(n+1) = FIR [ k(n), P(n), k(n-1), P(n-1), … ]
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Population Dynamics
Population Dynamics
Macroeconomy
Food Demand
Food Supply
106
%
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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
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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
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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.
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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.