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Mathematical Modeling using Fuzzy Logic:Applications to Sustainability
Rule-Based Fuzzy Logic Systems
New Concepts and Their Historical Background
Fundamental Diamond Requirement
The Flow of Uncertainties
Existing Literature on Type 2 Fuzzy Sets
Coverage
Applicability Outside of Rule-Based FLS
Computation
Primer on Fuzzy Sets
Fuzzy Sets
From Fuzzy Sets to Crisp Sets
Linguistic Variables
Membership Functions
Some Terminology
Set-Theoretic Operations on Crisp Sets
Set-Theoretic Operations for Fuzzy Sets
Crisp Relations and Compositions on the Same Product Space
Relations and Compositions
Hedges
Expansion Principle
FL Primer
Crisp Logic
From Crisp Logic to FL
Remarks
Exercise
References
Sources of Uncertainty
Uncertainty
Uncertainty: General Discussion
Uncertainty at FLS
Words Mean Different Things to Different People
Exercise
References
Membership Functions and Uncertainty
Introduction
Type 1 Membership Function
The Concept of a Type 2 Fuzzy Set
Definition of Type 2 Fuzzy Sets and Related Concepts
Type 2 Fuzzy Sets and Examples of FOU
Upper and Lower Membership Functions
A Type 1 Purge Set Represented by a Type 2 Fuzzy Set
and 1 Membership of Type 2 Fuzzy Set
Back to the Language Label
Exercise
References
Case Studies
Introduction
Time Series Prediction
Extracting Rules from Data
Classic Time Series Forecasting Method
Autoregression (AR)
Moving Average (MA)
Autoregressive Movement Average Type (ARMA)
Autoregressive Integrated Moving Average (ARIMA)
Seasonal Autoregressive Integrated Moving Average (SARIMA)
Vector Autoregression (VAR)
Vector Autoregressive Moving Average (VARMA)
Vector Autoregression Moving-Average with Exogenous Regressors (VARMAX)
Simple Exponential Smoothing (SES)
Holt–Winters Exponential Smoothing (HWES)
Knowledge Mining Using Surveys
Knowledge Mining Methodology
Exercise
References
Singleton Type 1 Fuzzy Logic Systems: No Uncertainties
Introduction
Rules
Fuzzy Inference Engine
Fuzzification and Its Effect on Reasoning
Fuzzifier
Defuzzification
Centroid Defuzzifier
Bisecting Defuzzifier
Weighted Average Defuzzifier
Midpoint of Maximum Defuzzifier
Largest of Maximum Defuzzifier
Smallest Maximum Defuzzifier
FLS Design
Back-Propagation (the Steepest Descent) Method
SVD-QR Method
Repetitive Diamond Method
Sample Study: Time Series Prediction
Case Study: Data Mining
Exercise
References
Centroid of a Type 2 Fuzzy Set: Type Reduction
Introduction
Unspecified Consequences for the Center
Generalization Center for Interval Type 2 Fuzzy Set
Interval Type 2 Center of Fuzzy Set
Type Reduction: Unspecified Consequences
Center Type Reduction
Height Type Reduction
Set Center Type Reduction
Computational Complexity of Type Reduction
Conclusion
Exercise
References
Modeling of Sustainability
The Meaning of Sustainability
Introduction to Sustainability by Fuzzy Assessment (SAFE) Model
SAFE Model Overview
Key Indicators of Sustainable Development
Measuring Sustainability
Fuzzy Assessment
Sensitivity Analysis
Advantages and Disadvantages of the SAFE Model
Sample Study for the SAFE Model
SAFE for Energy Sustainability
Conclusion
Exercise
References
Epilogue
Introduction
Type 2 vs. Type 1 FLS
Application for Type 2 FLS
Rule-Based Nomenclature for Video Traffic
Selected Function
FOU on Function
Rules
FOU for Measurement
FL RBC’s Parameters
Calculation Formula for Type 1 FL RBC
Calculation Formula for Type 2 FL RBC
Optimization of Rule Design Parameters
FL RBC Test
Results and Conclusions
Equalization of Time-Varying Nonlinear Digital Contacts
Preparation for Equalization of Water Supply
Why Type 2 FAFs Are Needed?
FAF Design
Simulation and Conclusion
Liaison System with ISI and CCI
Connection Ticket Rental for ATM Networks
Survey-Based CAC Using Type 2 FLS: Overview
Extraction of Knowledge for CAC
Survey Process
CAC Visualization Boundaries and Results
Exercise
References
Appendix A: Join, Meet, and Negation Operations for Non-Interval Type 2 Fuzzy Sets
Appendix B: Properties of Type 1 and Type 2 Fuzzy Sets
Appendix C: Computation
Appendix D: Medical Diagnosis by Fuzzy Logic
Appendix E: Fuzzy Logic System Optimized
Appendix F: Heart Disease Demo
Appendix G: Linear Tip Demo, Mamdani Tip Demo, Sugeno Tip Demo
Appendix H: Miscellaneous
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