Fuzzy Logic with Engineering Applications

Title Page
Copyright
Contents
About the Author
Preface to the Fourth Edition
Chapter 1 Introduction
	The Case for Imprecision
	A Historical Perspective
	The Utility of Fuzzy Systems
	Limitations of Fuzzy Systems
	The Illusion: Ignoring Uncertainty and Accuracy
	Uncertainty and Information
	Fuzzy Sets and Membership
	Chance versus Fuzziness
	Intuition of Uncertainty: Fuzzy versus Probability
	Sets as Points in Hypercubes
	Summary
	References
	Problems
Chapter 2 Classical Sets and Fuzzy Sets
	Classical Sets
		Operations on Classical Sets
		Properties of Classical (Crisp) Sets
		Mapping of Classical Sets to Functions
	Fuzzy Sets
		Fuzzy Set Operations
		Properties of Fuzzy Sets
		Alternative Fuzzy Set Operations
	Summary
	References
	Problems
Chapter 3 Classical Relations and Fuzzy Relations
	Cartesian Product
	Crisp Relations
		Cardinality of Crisp Relations
		Operations on Crisp Relations
		Properties of Crisp Relations
		Composition
	Fuzzy Relations
		Cardinality of Fuzzy Relations
		Operations on Fuzzy Relations
		Properties of Fuzzy Relations
		Fuzzy Cartesian Product and Composition
	Tolerance and Equivalence Relations
		Crisp Equivalence Relation
		Crisp Tolerance Relation
	Fuzzy Tolerance and Equivalence Relations
	Value Assignments
		Cosine Amplitude
		Max–Min Method
		Other Similarity Methods
	Other Forms of the Composition Operation
	Summary
	References
	Problems
Chapter 4 Properties of Membership Functions, Fuzzification, and Defuzzification
	Features of the Membership Function
	Various Forms
	Fuzzification
	Defuzzification to Crisp Sets
	λ-Cuts for Fuzzy Relations
	Defuzzification to Scalars
	Summary
	References
	Problems
Chapter 5 Logic and Fuzzy Systems
	Part I: Logic
	Classical Logic
		Tautologies
		Contradictions
		Equivalence
		Exclusive Or and Exclusive Nor
		Logical Proofs
		Deductive Inferences
	Fuzzy Logic
		Approximate Reasoning
		Other Forms of the Implication Operation
	Part II: Fuzzy Systems
		Natural Language
		Linguistic Hedges
		Fuzzy (Rule-Based) Systems
		Aggregation of Fuzzy Rules
		Graphical Techniques of Inference
	Summary
	References
	Problems
Chapter 6 Historical Methods of Developing Membership Functions
	Membership Value Assignments
	Intuition
	Inference
	Rank Ordering
	Neural Networks
	Genetic Algorithms
	Inductive Reasoning
	Summary
	References
	Problems
Chapter 7 Automated Methods for Fuzzy Systems
	Definitions
	Batch Least Squares Algorithm
	Recursive Least Squares Algorithm
	Gradient Method
	Clustering Method
	Learning from Examples
	Modified Learning from Examples
	Summary
	References
	Problems
Chapter 8 Fuzzy Systems Simulation
	Fuzzy Relational Equations
	Nonlinear Simulation Using Fuzzy Systems
	Fuzzy Associative Memories (FAMs)
	Summary
	References
	Problems
Chapter 9 Decision Making with Fuzzy Information
	Fuzzy Synthetic Evaluation
	Fuzzy Ordering
	Nontransitive Ranking
	Preference and Consensus
	Multiobjective Decision Making
	Fuzzy Bayesian Decision Method
	Decision Making under Fuzzy States and Fuzzy Actions
		Example Summary
	Summary
	References
	Problems
Chapter 10 Fuzzy Classification and Pattern Recognition
	Fuzzy Classification
	Classification by Equivalence Relations
		Crisp Relations
		Fuzzy Relations
	Cluster Analysis
	Cluster Validity
	c-Means Clustering
	Hard c-Means (HCM)
	Fuzzy c-Means (FCM)
		Fuzzy c-Means Algorithm
	Classification Metric
	Hardening the Fuzzy c-Partition
	Similarity Relations from Clustering
	Fuzzy Pattern Recognition
	Single-Sample Identification
	Multifeature Pattern Recognition
	Summary
	References
	Problems
Chapter 11 Fuzzy Control Systems
	Control System Design Problem
		Control (Decision) Surface
		Assumptions in a Fuzzy Control System Design
		Simple Fuzzy Logic Controllers
	Examples of Fuzzy Control System Design
		Aircraft Landing Control Problem
	Fuzzy Engineering Process Control
		Classical Feedback Control
		Classical PID Control
		Fuzzy Control
		Multi-Input, Multi-Output (MIMO) Control Systems
	Fuzzy Statistical Process Control
		Measurement Data: Traditional SPC
			Plant Simulation
			Establishing Fuzzy Membership Values
		Attribute Data: Traditional SPC
	Industrial Applications
	Summary
	References
	Problems
Chapter 12 Applications of Fuzzy Systems Using Miscellaneous Models
	Fuzzy Optimization
		One-Dimensional Optimization
	Fuzzy Cognitive Mapping
		Concept Variables and Causal Relations
		Paths and Cycles
		Indirect Effect
		Total Effect
		Indeterminacy
		Fuzzy Cognitive Maps
		Adjacency Matrix
		Threshold Function
		Feedback
		Min–Max Inference Approach
		Genetically Evolved Fuzzy Cognitive Maps
	Agent-Based Models
	Fuzzy Arithmetic and the Extension Principle
		Extension Principle
		Crisp Functions, Mapping, and Relations
		Functions of Fuzzy Sets: Extension Principle
	Fuzzy Algebra
		Fuzzy Arithmetic
	Data Fusion
		Kalman Filter in Data Fusion
	Summary
	References
	Problems
Chapter 13 Monotone Measures: Belief, Plausibility, Probability, and Possibility
	Monotone Measures
	Belief and Plausibility
	Evidence Theory
	Probability Measures
	Possibility and Necessity Measures
	Possibility Distributions as Fuzzy Sets
	Possibility Distributions Derived from Empirical Intervals
		Deriving Possibility Distributions from Overlapping Intervals
		Redistributing Weight from Nonconsonant to Consonant Intervals
		Comparison of Possibility Theory and Probability Theory
	Summary
	References
	Problems
Index
EULA