Mathematical Modeling using Fuzzy Logic: Applications to Sustainability

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface
Acknowledgments
Author
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
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
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
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 Method
			4.2.2.1 Autoregression (AR)
			4.2.2.2 Moving Average (MA)
			4.2.2.3 Autoregressive Movement 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
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
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
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
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
	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
Index