
Applications of Fuzzy Techniques
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This book is of interest to practitioners, researchers and graduate students seeking to apply existing techniques, to learn about the state of the art, or to explore novel concepts, in the theory and application of fuzzy sets and logic. Human knowledge and judgement are essential in both designing technological systems and in evaluating their outcomes. However, humans think and communicate in imprecise concepts, not numbers. Fuzzy sets and logic are well-known, widely used approaches to bridging this gap, which have been studied for nearly 60 years.
NAFIPS 2022 brought together researchers studying both the theoretical foundations of fuzzy logic and its application to real-world problems. Their work examined fuzzy solutions to problems as diverse as astronomy, chemical engineering, economics, energy engineering, health care, and transportation engineering. Many papers combined fuzzy logic with interval or probabilistic computing, neural networks, and genetic algorithms.
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Content
- Intro
- Preface
- Contents
- How to Elicit Complex-Valued Fuzzy Degrees
- 1 Formulation of the Problem
- 2 Analysis of the Problem
- 3 So How to Elicit Complex-Valued Fuzzy Degrees: Algorithm and Discussion
- 4 Conclusions
- References
- Flutter Mitigation via Fuzzy Gain Scheduling of a Passivity-Based Controller
- 1 Introduction
- 1.1 Problem
- 1.2 Genetic Fuzzy Control
- 1.3 Benchmark Aerodynamic Controls Technology Model
- 2 Methodology
- 2.1 Standard Controller
- 2.2 Fuzzy Gain Scheduled Controller
- 3 Results and Discussion
- 4 Conclusions
- References
- A New Weighting Method in Fuzzy Multi-criteria Decision Making: Selected Element Reduction Approach (SERA)
- 1 Introduction
- 2 Preliminaries
- 3 Methodology
- 4 Application
- 5 Conclusion
- References
- Genetic Fuzzy System for Pitch Control on a F-4 Phantom
- 1 Introduction
- 2 F-4 Fighter Pitch Angle Dynamic Behavior
- 3 Genetic Takagi-Sugeno-Kang Fuzzy Inference System
- 4 Conclusions and Future Works
- References
- Analyzing the Sars-Cov-2 Pandemic Outbreak Using Fuzzy Sets and the SIR Model
- 1 Introduction
- 2 The Sars-Cov-2 Pandemic
- 3 Basic Concepts on Fuzzy Sets
- 4 SIR Model
- 4.1 Fuzzy Solution and Asymptotic Behavior
- 4.2 Time-Varying Basic Reproductive Number
- 5 Application to Sars-Cov-2 Outbreak
- 5.1 Results
- 5.2 Comparing and Forecasting
- 6 Conclusion
- References
- Hybrid Fuzzy-LQR Control for Time Optimal Spacecraft Docking
- 1 Introduction
- 1.1 Related Work
- 2 Background
- 2.1 Linear Quadratic Regulator Control
- 2.2 Fuzzy-Based Bang-Bang Control
- 2.3 Genetic Algorithms
- 3 Methodology
- 3.1 Spacecraft Docking Problem
- 3.2 GA Approach
- 3.3 LQR Controller Approach
- 3.4 Fuzzy-Based Bang-Bang Controller Approach
- 3.5 Hybrid Fuzzy-LQR Controller Approach
- 4 Results
- 5 Conclusion
- References
- An Experimental Study on Fuzzy Markov Chains Under Mn Generalized Mean Relation
- 1 Introduction and Motivation
- 2 Fuzzy Markov Chains
- 2.1 Normalized Fuzzy Transition Matrix
- 2.2 Mn Generalized Mean and Its Use in Computing the Limiting Distribution of P
- 3 Illustrative Examples
- 3.1 Discussion of the Results
- 4 Concluding Remarks
- References
- An Approach to Simulation of Fuzzy Linguistic Variables
- 1 Introduction and Motivation
- 2 Basics on Fuzzy Numbers
- 2.1 Fuzzy Linguistic Variables
- 3 An Approach to Fuzzy Linguistic Random Variate Generation
- 3.1 Fuzzy Random Variate Generation for Linguistic Variables
- 3.2 Fuzzy Random Linguistic Value Generation
- 3.3 Fuzzy Random Variate Generation
- 4 Illustrative Example
- 5 Concluding Remarks
- References
- Why Sine Membership Functions
- 1 Formulation of the Problem
- 2 Our Explanation
- 3 Conclusions
- References
- Agricultural Yield Prediction by Difference Equations on Data-Induced Cumulative Possibility Distributions
- 1 Introduction
- 2 Mathematical Background
- 2.1 Elementary Lattice Theory Definitions
- 2.2 The Cone of Intervals' Numbers (INs) and a Novel Interpretation
- 2.3 Differential Intervals' Number (IN) Models
- 3 Novel Algorithms
- 3.1 Difference Intervals' Number (IN) Models
- 3.2 Algorithms for Training and Testing
- 4 Experiments and Results
- 4.1 Data Acquisition
- 4.2 Data Preprocessing and Experiments
- 4.3 Discussion
- 5 Conclusion
- References
- Commonsense-Continuous Dynamical Systems - Stationary States, Prediction, and Reconstruction of the Past: Fuzzy-Based Analysis
- 1 Formulation of the Problem
- 2 Mathematical Continuity vs. Commonsense Continuity: Analysis of the Difference
- 3 Useful Corollary
- 4 Auxiliary Corollaries: Predicting the Future and Reconstructing the Past
- 5 Conclusions
- References
- Why Gaussian Copulas Are Ubiquitous in Economics: Fuzzy-Related Explanation
- 1 Formulation of the Problem
- 2 Analysis of the Problem and the Resulting Explanation
- References
- A Note on Caputo Fractional Derivative in the Space of Linearly Correlated Fuzzy Numbers
- 1 Introduction
- 2 Preliminaries
- 2.1 Interactivity
- 2.2 The Space RF(A)
- 3 Caputo Derivative in RF(A)
- 4 Fractional Logistic Model in RF(A) for Cumulative Cases of COVID-19
- 5 Conclusion
- References
- Data Driven Level Set Method in Fuzzy Modeling and Forecasting
- 1 Introduction
- 2 Data Driven Level Set Method
- 3 Model Accuracy and Transparency
- 4 Electric Power Load Forecasting
- 5 Conclusion
- References
- Semi-supervised Physics-Informed Genetic Fuzzy System for IoT BLE Localization
- 1 Introduction
- 2 Background
- 3 Dataset Description
- 4 Methodology
- 4.1 Semi-supervised Label Propagation
- 4.2 Physics-Informed Genetic Fuzzy System
- 5 Results and Discussion
- 6 Conclusion
- References
- The Constraint Interval Theory: A Solution for Interval Differential Equations
- 1 Introduction
- 2 Standard Interval Arithmetic and Constraint Interval Arithmetic
- 3 Solution of Initial Value Problem for Interval Linear Differential Equations System
- 4 Conclusion
- References
- Classification of Rice Using Genetic Fuzzy Cascading System
- 1 Introduction
- 1.1 Need of Fuzzy Techniques for Explainable AI (XAI)
- 1.2 Genetic Fuzzy Systems and Cascading
- 1.3 Classification of Rice
- 2 Methodology
- 2.1 Fuzzy Inference System (FIS)
- 2.2 Fuzzy Cascading
- 2.3 Genetic Algorithm
- 3 Results
- 4 Conclusion
- 4.1 Challenges and Future Work
- References
- On a New Contrapositivisation Technique for Fuzzy Implications Constructed from Grouping Functions
- 1 Introduction
- 2 Preliminaries
- 3 Contrapositivisation Techniques
- 4 (G,N)-Contrapositivisation
- 5 Final Remarks
- References
- Genetically Trained Fuzzy Cognitive Maps for Effects Based Operations
- 1 Introduction
- 2 Methodology
- 2.1 Forward Propagating Knowledge Graph Solution
- 2.2 Genetic Source-Determination Knowledge Graph Solution
- 2.3 Fuzzy Inference System Integration
- 3 Results and Discussion
- 3.1 Forward Propagating Solver Results
- 3.2 Genetic Source-Determination Results
- 4 Conclusions and Future Work
- References
- Genetic Fuzzy Controller for the Homicidal Chauffeur Differential Game
- 1 Introduction
- 1.1 Related Work on the Homicidal Chauffeur
- 2 Methodology
- 2.1 Optimal Control Solution
- 2.2 Genetic Fuzzy System
- 2.3 Noise Addition
- 3 Results
- 3.1 Results of Noise Added
- 4 Discussion
- 5 Summary and Conclusions
- References
- Use of Fuzzy PID Controller for Pitch Control of a Wind Turbine
- 1 Introduction
- 2 Background and Preliminaries
- 2.1 Wind Turbine Model
- 2.2 Genetic Algorithm
- 2.3 Genetic Fuzzy System
- 3 Methodology
- 4 Results
- 5 Conclusion and Future Works
- References
- Special Tolerance Left Solution for Course Assignment Problem with Interval Workload Constraint
- 1 Introduction
- 2 Special Tolerance Left Solution to System of Interval Linear Equations
- 2.1 Definition and Characteristics of Tolerance Solution to System of Interval Linear Equations
- 2.2 Definition and Characteristics of Special Tolerance Left Solution to System of Interval Linear Equations
- 3 Course Assignment Problem with Interval Workload Constraint
- 4 Results
- 5 Conclusion
- References
- Passive Fault-Tolerant Control Scheme for Nonlinear Level Control System with Parameter Uncertainty and Actuator Fault
- 1 Introduction
- 2 Uncertain Benchmark Level Control System
- 2.1 Uncertain Benchmark Two-Tank Level Control System
- 2.2 Benchmark Two-Tank Level Control System Mathematical Modeling
- 3 Proposed Methodology for Passive FTC
- 3.1 Data Generation Layer
- 3.2 Pre-processing Layer
- 3.3 Training Layer
- 4 Implementation and Results
- 4.1 Implementation Setup
- 4.2 Simulation Results
- 5 Conclusion and Future Work
- References
- Can Physically-Trained Genetic Fuzzy Learning Algorithm Improve Pitch Control in Wind Turbines?
- 1 Introduction
- 2 WT Model
- 3 Genetic Fuzzy Methodology
- 3.1 Genetic Algorithm
- 3.2 Training the GFS
- 3.3 Structure of the GFS
- 4 Results
- 4.1 Training the GFS
- 4.2 Testing the GFS
- 5 Conclusions and Future Work
- References
- Generating Interval Type-2 Fuzzy Inputs from Smoothed Data for Fuzzy Rule-Based Systems
- 1 Introduction
- 2 Some Background Information
- 2.1 Type-1 and Type-2 Fuzzy Sets
- 2.2 Non-Singleton Fuzzy Logic Systems
- 2.3 Smoothing Using Penalized Least Squares Regression
- 2.4 Signal-to-Noise Ratio
- 3 Problem Statement and Methodology
- 3.1 Algorithm 1: Stable Noise in Both Training and Test Sets
- 3.2 Algorithm 2: Varying Noise Levels in the Application Phase
- 4 Experimental Results in Time Series Prediction
- 5 Concluding Remarks
- References
- Subsethood Measures on a Bounded Lattice of Continuous Fuzzy Numbers with an Application in Approximate Reasoning
- 1 Introduction
- 2 Some Mathematical Background on Lattice Theory and Subsethood Measures
- 3 Some Facts Regarding Subsethood and Inclusion Measures
- 4 A Bounded Lattice of Continuous Fuzzy Numbers for Analogical Reasoning
- 5 An Outline of an Application in Mechanical Condition Monitoring
- 6 Conclusions
- References
- Why Ideas First Appear in Informal Form? Why It Is Very Difficult to Know Yourself? Fuzzy-Based Explanation
- 1 Formulation of the Problem
- 2 Analysis of the Problem Explains the Need for Informal Ideas
- 3 From This Viewpoint, Measurement Errors Are the Blessing in Disguise
- 4 Why Is It Difficult to Know Oneself
- 5 How Can All This Be Used
- References
- Pulsar Candidate Selection Using a Genetic Fuzzy System
- 1 Introduction
- 2 Background
- 2.1 Pulsar Candidate Generation
- 2.2 Pulsar Candidate Selection
- 2.3 Pulsar Data Set
- 3 Methodology
- 3.1 Genetic Fuzzy Tree
- 3.2 Genetic Algorithm
- 3.3 Training and Testing
- 4 Results and Discussion
- 5 Conclusions
- References
- Single Hidden Layer CEFYDRA: Cluster-first Explainable FuzzY-based Deep self-Reorganizing Algorithm
- 1 Introduction
- 2 Introduction of the Architecture
- 3 Update Rules for Hidden Layer Parameters
- 4 Conclusions
- References
- Multiple Hidden Layered CEFYDRA: Cluster-First Explainable Fuzzy-Based Deep Self-reorganizing Algorithm
- 1 Introduction
- 2 On the Learning Formulas for the Hidden Layer
- 3 On How to Perform the Update While Minimizing the Calculations
- 4 Conclusions
- References
- Initialization and Plasticity of CEFYDRA: Cluster-first Explainable FuzzY-based Deep self-Reorganizing Algorithm
- 1 Introduction
- 2 On How to Initialize the Parameters Without Prior Knowledge of the Hidden Features
- 2.1 Initialization of the Cauchy Membership Functions
- 2.2 Initialization of the Logistic Functions
- 3 On the Plasticity of CEFYDRA
- 4 Conclusions
- References
- Synthesis Chemical Reaction Model via P-Fuzzy Systems
- 1 Introduction
- 2 Method
- 2.1 Fuzzy Rule-Based System
- 2.2 Partially Fuzzy System
- 3 Application
- 4 Final Remarks
- References
- Proposal of a Novel Python-Based Fuzzy Systems Library - Preliminary Results
- 1 Introduction
- 2 Related Work
- 3 Preliminaries
- 3.1 Fuzzy Systems
- 3.2 Mamdani to Takagi-Sugeno-Kang Representation
- 3.3 Mamdani Approximation of a TSK System. One Antecedent Case
- 3.4 Mamdani Approximation of a TSK System. Multiple Antecedent Case
- 4 Library Description
- 4.1 Architecture Overview
- 4.2 Defining Membership Functions, Groups, and Groupsets
- 4.3 Defining Rules and Rulesets
- 4.4 Performing Mamdani and Takagi-Sugeno-Kang Inference
- 4.5 Fuzzy Network Definition and Evaluation
- 4.6 Approximating Mamdani Membership Functions
- 5 Examples
- 5.1 Temperature
- 5.2 Tipping
- 6 Conclusion and Further Research
- References
- Author Index
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