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