Fuzzy Inductive Reasoning

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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

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System Dynamics

• Levels and Rates

• Laundry List

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System Dynamics

• Levels and Rates
• Laundry List

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Modeling Methodologies
Knowledge-Based Approaches
Pattern-Based Approaches
Deep Models
Shallow Models
Neural Networks
Inductive 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
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 Reasoning
Mixed Quantitative/Qualitative Modeling
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Application
Cardiovascular System
Central Nervous System Control (Qualitative Model)
Hemodynamical System (Quantitative Model)
Heart Rate Controller
Heart
Myocardiac Contractility Controller
Peripheric Resistance Controller
Circulatory Flow Dynamics
Venous Tone Controller
Carotid Sinus Blood Pressure
Coronary Resistance Controller
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 doesnt
  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
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Population Dynamics

• Predicting Growth Functions

k(n1) FIR k(n), P(n), k(n-1), P(n-1),
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Population Dynamics

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Macroeconomy


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Macroeconomy


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Food Demand/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_f
  ir.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
  doesnt suffer from scale-up problems.