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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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System Dynamics Levels and Rates

Laundry List

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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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Cardiovascular SystemConfidence Computation

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Cardiovascular SystemConfidence Computation

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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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Fuzzification in FIR

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Qualitative Simulation

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Food Demand Modeling

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Population Dynamics

Population Dynamics

Macroeconomy

Food Demand

Food Supply

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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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Macroeconomy

Population Dynamics

Macroeconomy

Food Demand

Food Supply

$

%

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Macroeconomy

Population Dynamics

Macroeconomy

Food Demand

Food Supply

%

%

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Food Demand/Supply

Population Dynamics

Macroeconomy

Food Demand

Food Supply

£

%

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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.