Mathematical Modeling using Fuzzy Logic 1st Edition by Abhijit Pandit ISBN 0429751710 9780429751714

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ISBN 10:      0429751710
ISBN 13: 978-0429751714
Author:      Abhijit Pandit

Mathematical Modeling using Fuzzy Logic 1st Table of contents:

1. Introduction

• 1.1 Rule-Based Fuzzy Logic Systems
• 1.2 A New Direction for FLSs
• 1.3 New Concepts and Their Historical Background
• 1.4 Fundamental Diamond Requirement
• 1.5 The Flow of Uncertainties
• 1.6 Existing Literature on Type 2 Fuzzy Sets
• 1.7 Coverage
• 1.8 Applicability Outside of Rule-Based FLS
• 1.9 Computation
• 1.10 Primer on Fuzzy Sets
  • 1.10.1 Fuzzy Sets
  • 1.10.2 From Fuzzy Sets to Crisp Sets
  • 1.10.3 Linguistic Variables
  • 1.10.4 Membership Functions
  • 1.10.5 Some Terminology
  • 1.10.6 Set-Theoretic Operations on Crisp Sets
  • 1.10.7 Set-Theoretic Operations for Fuzzy Sets
  • 1.10.8 Crisp Relations and Compositions on the Same Product Space
  • 1.10.9 Relations and Compositions
  • 1.10.10 Hedges
  • 1.10.11 Expansion Principle
• 1.11 FL Primer
  • 1.11.1 Crisp Logic
  • 1.11.2 From Crisp Logic to FL
• 1.12 Remarks
• 1.13 Exercise
• References

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2. Sources of Uncertainty

• 2.1 Uncertainty
  • 2.1.1 Uncertainty: General Discussion
  • 2.1.2 Uncertainty at FLS
• 2.2 Words Mean Different Things to Different People
• 2.3 Exercise
• References

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3. Membership Functions and Uncertainty

• 3.1 Introduction
• 3.2 Type 1 Membership Function
  • 3.2.1 The Concept of a Type 2 Fuzzy Set
  • 3.2.2 Definition of Type 2 Fuzzy Sets and Related Concepts
  • 3.2.3 Type 2 Fuzzy Sets and Examples of FOU
  • 3.2.4 Upper and Lower Membership Functions
  • 3.2.5 A Type 1 Purge Set Represented by a Type 2 Fuzzy Set
  • 3.2.6 0 and 1 Membership of Type 2 Fuzzy Set
• 3.3 Back to the Language Label
• 3.4 Exercise
• References

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4. Case Studies

• 4.1 Introduction
• 4.2 Time Series Prediction
  • 4.2.1 Extracting Rules from Data
  • 4.2.2 Classic Time Series Forecasting Methods
    • 4.2.2.1 Autoregression (AR)
    • 4.2.2.2 Moving Average (MA)
    • 4.2.2.3 Autoregressive Moving Average Type (ARMA)
    • 4.2.2.4 Autoregressive Integrated Moving Average (ARIMA)
    • 4.2.2.5 Seasonal Autoregressive Integrated Moving Average (SARIMA)
    • 4.2.2.6 Seasonal Autoregressive Integrated Moving Average (SARIMAX) Using Exogenous Regression Variables
    • 4.2.2.7 Vector Autoregression (VAR)
    • 4.2.2.8 Vector Autoregressive Moving Average (VARMA)
    • 4.2.2.9 Vector Autoregression Moving-Average with Exogenous Regressors (VARMAX)
    • 4.2.2.10 Simple Exponential Smoothing (SES)
    • 4.2.2.11 Holt–Winters Exponential Smoothing (HWES)
• 4.3 Knowledge Mining Using Surveys
  • 4.3.1 Knowledge Mining Methodology
• 4.4 Exercise
• References

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5. Singleton Type 1 Fuzzy Logic Systems: No Uncertainties

• 5.1 Introduction
• 5.2 Rules
• 5.3 Fuzzy Inference Engine
• 5.4 Fuzzification and Its Effect on Reasoning
  • 5.4.1 Fuzzifier
• 5.5 Defuzzification
  • 5.5.1 Centroid Defuzzifier
  • 5.5.2 Bisecting Defuzzifier
  • 5.5.3 Weighted Average Defuzzifier
  • 5.5.4 Midpoint of Maximum Defuzzifier
  • 5.5.5 Largest of Maximum Defuzzifier
  • 5.5.6 Smallest Maximum Defuzzifier
• 5.6 FLS Design
  • 5.6.1 Back-Propagation (the Steepest Descent) Method
  • 5.6.2 SVD-QR Method
  • 5.6.3 Repetitive Diamond Method
• 5.7 Sample Study: Time Series Prediction
• 5.8 Case Study: Data Mining
• 5.9 Exercise
• References

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6. Centroid of a Type 2 Fuzzy Set: Type Reduction

• 6.1 Introduction
• 6.2 Unspecified Consequences for the Center
• 6.3 Generalization Center for Interval Type 2 Fuzzy Set
• 6.4 Interval Type 2 Center of Fuzzy Set
• 6.5 Type Reduction: Unspecified Consequences
  • 6.5.1 Center Type Reduction
  • 6.5.2 Height Type Reduction
  • 6.5.3 Set Center Type Reduction
  • 6.5.4 Computational Complexity of Type Reduction
  • 6.5.5 Conclusion
• 6.6 Exercise
• References

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7. Modeling of Sustainability

• 7.1 The Meaning of Sustainability
• 7.2 Introduction to Sustainability by Fuzzy Assessment (SAFE) Model
• 7.3 SAFE Model Overview
• 7.4 Key Indicators of Sustainable Development
• 7.5 Measuring Sustainability
• 7.6 Fuzzy Assessment
• 7.7 Sensitivity Analysis
• 7.8 Advantages and Disadvantages of the SAFE Model
• 7.9 Sample Study for the SAFE Model
  • 7.9.1 SAFE for Energy Sustainability
• 7.10 Conclusion
• 7.11 Exercise
• References

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8. Epilogue

• 8.1 Introduction
• 8.2 Type 2 vs. Type 1 FLS
• 8.3 Application for Type 2 FLS
• 8.4 Rule-Based Nomenclature for Video Traffic
  • 8.4.1 Selected Function
  • 8.4.2 FOU on Function
  • 8.4.3 Rules
  • 8.4.4 FOU for Measurement
  • 8.4.5 FL RBC’s Parameters
  • 8.4.6 Calculation Formula for Type 1 FL RBC
  • 8.4.7 Calculation Formula for Type 2 FL RBC
  • 8.4.8 Optimization of Rule Design Parameters
  • 8.4.9 FL RBC Test
  • 8.4.10 Results and Conclusions
• 8.5 Equalization of Time-Varying Nonlinear Digital Contacts
  • 8.5.1 Preparation for Equalization of Water Supply
  • 8.5.2 Why Type 2 FAFs Are Needed?
  • 8.5.3 FAF Design
  • 8.5.4 Simulation and Conclusion
• 8.6 Liaison System with ISI and CCI
• 8.7 Connection Ticket Rental for ATM Networks
  • 8.7.1 Survey-Based CAC Using Type 2 FLS: Overview
  • 8.7.2 Extraction of Knowledge for CAC
  • 8.7.3 Survey Process
  • 8.7.4 CAC Visualization Boundaries and Results
• 8.8 Exercise

 

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