Transcript Fuzzy Inductive Reasoning
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.
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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 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
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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.
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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)
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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
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Cardiovascular System
Confidence Computation
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Cardiovascular System
Confidence 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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Food Supply Food Demand Macroeconomy Population Dynamics
Population Dynamics
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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), … ]
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Population Dynamics
10 6
Food Supply Food Demand Macroeconomy Population Dynamics
%
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Macroeconomy
$
Food Supply Food Demand Macroeconomy Population Dynamics
%
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Food Supply Food Demand Macroeconomy Population Dynamics
Macroeconomy
% %
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Food Demand/Supply
£
Food Supply Food Demand Macroeconomy Population Dynamics
%
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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
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
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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
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.
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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.
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