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.

Jump to first page

Contents

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

System Dynamics

 Levels and Rates

Levels Rates Inflows Outflows

Population Money Frustration Love Tumor Cells Inventory on Stock Knowledge Birth Rate Income Stress Affection Infection Shipments Learning Death Rate Expenses Affection Frustration Treatment Sales Forgetting  Laundry List

Birth Rate:

• Population • Material Standard of Living • Food Quality • Food Quantity • Education • Contraceptives • Religious Beliefs Jump to first page

System Dynamics

 Levels and Rates  Laundry List Jump to first page

Modeling Methodologies

Deep Models Knowledge-Based Approaches Shallow Models Pattern-Based Approaches Inductive Reasoners

FIR

Neural Networks

Jump to first page

Inductive Modeling Techniques

 Making Models from Observations of Input/Output Behavior  Understanding Systems  Forecasting Systems Behavior  Controlling Systems Behavior Jump to first page

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.

Jump to first page

More Comparisons

Neural Networks

Quantitative Parametric Adaptive Slow Training Smooth Interpolation Wild Extrapolation No Error Estimate Unsafe / Gullible

Fuzzy Inductive R.

Qualitative Non-parametric Limited Adaptability Fast Setup Decent Interpolation No Extrapolation Error Estimate Robust / Self-critical Jump to first page

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)

Jump to first page

Fuzzy Inductive Reasoning

Mixed Quantitative/Qualitative Modeling

Quantitative Subsystem Recode Regenerate FIR Model Regenerate FIR Model Recode Quantitative Subsystem Jump to first page

Application

Cardiovascular System Central Nervous System Control (Qualitative Model)

Heart Rate Controller

Regenerate Hemodynamical System (Quantitative Model) Heart

Myocardiac Contractility Controller Peripheric Resistance Controller

Regenerate

Venous Tone Controller

Regenerate Regenerate Circulatory Flow Dynamics Carotid Sinus Blood Pressure

Coronary Resistance Controller

Regenerate Recode

Jump to first page

Cardiovascular System

Confidence Computation

Jump to first page

Cardiovascular System

Confidence Computation

Jump to first page

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.

Jump to first page

Fuzzification in FIR

Jump to first page

Qualitative Simulation

Jump to first page

Food Demand Modeling

Jump to first page

Food Supply Food Demand Macroeconomy Population Dynamics

Population Dynamics

Jump to first page

Population Dynamics

 Predicting Growth Functions Food Supply Food Demand Macroeconomy Population Dynamics

k(n+1) =

FIR

[ k(n), P(n), k(n-1), P(n-1), … ]

Jump to first page

Population Dynamics

10 6

Food Supply Food Demand Macroeconomy Population Dynamics

%

Jump to first page

Macroeconomy

$

Food Supply Food Demand Macroeconomy Population Dynamics

%

Jump to first page

Food Supply Food Demand Macroeconomy Population Dynamics

Macroeconomy

% %

Jump to first page

Food Demand/Supply

£

Food Supply Food Demand Macroeconomy Population Dynamics

%

Jump to first page

Applications

     Cardiovascular System Modeling for Classification of Anomalies Anaesthesiology Model for Control of Depth of Anaesthesia During Surgery Shrimp Growth Model for

El Remolino

in Northern M éxico Shrimp Farm 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 Jump to first page

    

Dissertations

Àngela Nebot (1994)

Simulation of Biomedical Systems Using Fuzzy Inductive Reasoning Qualitative Modeling and

Francisco Mugica

Inductivo

(1995)

Diseño Sistemático de Controladores Difusos Usando Razonamiento

Álvaro de Albornoz

Systems

(1996)

Inductive Reasoning and Reconstruction Analysis: Two Complementary Tools for Qualitative Fault Monitoring of Large-Scale

Josefina López

Reasoning

(1998)

Qualitative Modeling and Simulation of Time Series Using Fuzzy Inductive

Sebastián Medina (1998)

Knowledge Generalization from Observation

Jump to first page

Primary Publications

     F.E.Cellier

(1991)

Continuous System Modeling, Springer Verlag, New York.

F.E.Cellier, A.Nebot, F. Mugica, and A. de Albornoz

Continuous-Time Processes Using Fuzzy Inductive Reasoning Techniques,

Intl. J. General Systems.

(1996)

Combined Qualitative/Quantitative Simulation Models of

A. Nebot, F.E. Cellier, and M. Vallverdú

Cardiovascular System,

(1998)

Mixed Quantitative/Qualitative Modeling and Simulation of the

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.

Jump to first page

Conclusions

     Fuzzy Inductive Reasoning of behavior.

offers an exciting alternative to Neural Networks for modeling systems from observations 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 the methodology.

offers a

self-assessment

feature, which is easily the most important characteristic of 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.

Jump to first page