A Dynamical Fuzzy System with Linguistic Information Feedback

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A Dynamical Fuzzy System with Linguistic
Information Feedback

• Xiao-Zhi Gao and Seppo J. Ovaska
• Institute of Intelligent Power Electronics
• Department of Electrical and Communications
  Engineering
• Helsinki University of Technology, Finland

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Outline

• Introduction
• Basic Fuzzy Systems
• Conventional Dynamical Fuzzy Systems
• Fuzzy Systems with Linguistic Information
  Feedback
• Simulation Results
• Conclusions and Remarks

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Introduction

• Fuzzy logic theory has found successful
  applications in industrial engineering
• Most fuzzy systems applied in practice are static
• static input-output mappings
• no internal dynamics
• A new dynamical fuzzy model with linguistic
  information feedback is proposed
• suitable for dynamical system modeling, control,
  filtering, time series prediction, etc.

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Basic Fuzzy Systems
Feedforward Stucture (Mamdani Type) IF x is A AND
(OR) y is B THEN z is C
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Conventional Dynamical Fuzzy Systems

• Classical fuzzy systems lack necessary internal
  dynamics
• can only realize static mappings
• Feedback is needed to introduce dynamics
• Two kinds of conventional recurrent fuzzy systems
• Globally feedback fuzzy systems
• Locally feedback fuzzy systems
• Crisp information feedback

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Globally Feedback Fuzzy Systems
Output and Crisp Feedback
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Locally Feedback Fuzzy Systems
Internal Memory Units
Lee2000
Fuzzy Input Membership Functions
Crisp Output
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Crisp Information Feedback
Defuzzification Fuzzy-gtNonfuzzy
Conversion Unavoidable Information Lost
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Dynamical Fuzzy System with Linguistic
Information Feedback
Inference Output (Membership Function) is fed back
Mamdani Type
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Feedback Parameters
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Diagram of Fuzzy Information Feedback Scheme
Feedback is controlled by
Linguistic Information Feedback
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Linguistic Information Feedback for Individual
Fuzzy Rules
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High-Order Linguistic Information Feedback
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Learning Algorithms of Feedback Parameters

• Feedback parameters have a nonlinear relationship
  with system output
• It is difficult to derive an explicit learning
  algorithm
• Some general-purpose algorithms can be applied to
  optimize feedback parameters
• genetic algorithms (GA)

nonlinear operators
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Advantages of Linguistic Information Feedback

• 1. Rich fuzzy inference output is fed back
  without any information transformation and loss
• 2. Local feedback connections can store temporal
  patterns
• Suitable for dynamical system identification
• 3. Training of feedback coefficients leads to an
  equivalent update of output membership functions
• Benefit of adaptation

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Simulations

• A simple dynamical fuzzy system with linguistic
  information feedback
• single-input-single-output
• two inference rules
• IF X is Small THEN Y is Small
• IF X is Large THEN Y is Large
• max-min and sum-product composition
• COA defuzzification
• Step input ( )

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Input and Output Fuzzy Membership Functions
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Step Responses with First-Order Fuzzy Feedback
Solid line max-min composition.
Dotted line sum-product composition
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Step Response with Second-Order Fuzzy Feedback
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Time Sequence Prediction I
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Fuzzy Predictor with Linguistic Information
Feedback

• Four fuzzy rules are constructed
• IF x(k) is -1 THEN x(k1) is 0
• IF x(k) is 0 THEN x(k1) is 1
• IF x(k) is 1 THEN x(k1) is 0
• IF x(k) is 0 THEN x(k1) is -1
• Rule 2 and Rule 4 are conflicting
• Linguistic information feedback can correct

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Input Membership Functions of Fuzzy Predictor
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Evolution of GA-Based Feedback Parameters
Optimization
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Prediction Outputs of Fuzzy Predictors
Dotted line static fuzzy predictor. Solid line
dynamical fuzzy predictor
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Time Sequence Prediction II
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Output Membership Functions of Fuzzy Predictor
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Prediction Outputs of Fuzzy Predictors
Dotted line static fuzzy predictor. Solid line
dynamical fuzzy predictor
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Conclusions

• A new dynamical fuzzy system with linguistic
  information feedback is proposed
• Dynamical properties of our fuzzy model are shown
• Present paper is a starting point for our future
  work under this topic
• more simulations are needed
• extension to Sugeno type fuzzy sytems
• extension to feedforward structure
• extension to premise part
• applications in dynamical system identification