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by Udit Chakraborty, Samir Roy
Soft Computing
Cover
Title page
Contents
About the Authors
Dedication
Preface
Chapter 1: Introduction
1.1 What is Soft Computing?
1.2 Fuzzy Systems
1.3 Rough Sets
1.4 Artificial Neural Networks
1.5 Evolutionary Search Strategies
Chapter Summary
Test Your Knowledge
Answers
Exercises
Bibliography and Historical Notes
Chapter 2: Fuzzy Sets
2.1 Crisp Sets: A Review
2.1.1 Basic Concepts
2.1.2 Operations on Sets
2.1.3 Properties of Sets
2.2 Fuzzy Sets
2.2.1 Fuzziness/Vagueness/Inexactness
2.2.2 Set Membership
2.2.3 Fuzzy Sets
2.2.4 Fuzzyness vs. Probability
2.2.5 Features of Fuzzy Sets
2.3 Fuzzy Membership Functions
2.3.1 Some Popular Fuzzy Membership Functions
2.3.2 Transformations
2.3.3 Linguistic Variables
2.4 Operations on Fuzzy Sets
2.5 Fuzzy Relations
2.5.1 Crisp Relations
2.5.2 Fuzzy Relations
2.5.3 Operations on Fuzzy Relations
2.6 Fuzzy Extension Principle
2.6.1 Preliminaries
2.6.2 The Extension Principle
Chapter Summary
Solved Problems
Test Your Knowledge
Answers
Exercises
Bibliography and Historical Notes
Chapter 3: Fuzzy Logic
3.1 Crisp Logic: A Review
3.1.1 Propositional Logic
3.1.2 Predicate Logic
3.1.3 Rules of Inference
3.2 Fuzzy Logic Basics
3.2.1 Fuzzy Truth Values
3.3 Fuzzy Truth in Terms of Fuzzy Sets
3.4 Fuzzy Rules
3.4.1 Fuzzy If-Then
3.4.2 Fuzzy If-Then-Else
3.5 Fuzzy Reasoning
3.5.1 Fuzzy Quantifiers
3.5.2 Generalized Modus Ponens
3.5.3 Generalized Modus Tollens
Chapter Summary
Solved Problems
Test Your Knowledge
Answers
Exercises
Bibliography and Historical Notes
Chapter 4: Fuzzy Inference Systems
4.1 Introduction
4.2 Fuzzification of the Input Variables
4.3 Application of Fuzzy Operators on the Antecedent Parts of the Rules
4.4 Evaluation of the Fuzzy Rules
4.5 Aggregation of Output Fuzzy Sets Across the Rules
4.6 Defuzzification of the Resultant Aggregate Fuzzy Set
4.6.1 Centroid Method
4.6.2 Centre-of-Sums (CoS) Method
4.6.3 Mean-of-Maxima (MoM) Method
4.7 Fuzzy Controllers
4.7.1 Fuzzy Air Conditioner Controller
4.7.2 Fuzzy Cruise Controller
Chapter Summary
Solved Problems
Test Your Knowledge
Answers
Exercises
Bibliography and Historical Notes
Chapter 5: Rough Sets
5.1 Information Systems and Decision Systems
5.2 Indiscernibility
5.3 Set Approximations
5.4 Properties of Rough Sets
5.5 Rough Membership
5.6 Reducts
5.7 Application
Chapter Summary
Solved Problems
Test Your Knowledge
Answers
Exercises
Bibliography and Historical Notes
Chapter 6: Artificial Neural Networks: Basic Concepts
6.1 Introduction
6.1.1 The Biological Neuron
6.1.2 The Artificial Neuron
6.1.3 Characteristics of the Brain
6.2 Computation in Terms of Patterns
6.2.1 Pattern Classification
6.2.2 Pattern Association
6.3 The McCulloch–Pitts Neural Model
6.4 The Perceptron
6.4.1 The Structure
6.4.2 Linear Separability
6.4.3 The XOR Problem
6.5 Neural Network Architectures
6.5.1 Single Layer Feed Forward ANNs
6.5.2 Multilayer Feed Forward ANNs
6.5.3 Competitive Network
6.5.4 Recurrent Networks
6.6 Activation Functions
6.6.1 Identity Function
6.6.2 Step Function
6.6.3 The Sigmoid Function
6.6.4 Hyperbolic Tangent Function
6.7 Learning by Neural Nets
6.7.1 Supervised Learning
6.7.2 Unsupervised Learning
Chapter Summary
Solved Problems
Test Your Knowledge
Answers
Exercises
Bibliography and Historical Notes
Chapter 7: Pattern Classifiers
7.1 Hebb Nets
7.2 Perceptrons
7.3 ADALINE
7.4 MADALINE
Chapter Summary
Solved Problems
Test Your Knowledge
Answers
Exercises
Bibliography and Historical Notes
Chapter 8: Pattern Associators
8.1 Auto-associative Nets
8.1.1 Training
8.1.2 Application
8.1.3 Elimination of Self-connection
8.1.4 Recognition of Noisy Patterns
8.1.5 Storage of Multiple Patterns in an Auto-associative Net
8.2 Hetero-associative Nets
8.2.1 Training
8.2.2 Application
8.3 Hopfield Networks
8.3.1 Architecture
8.3.2 Training
8.4 Bidirectional Associative Memory
8.4.1 Architecture
8.4.2 Training
8.4.3 Application
Chapter Summary
Solved Problems
Test Your Knowledge
Answers
Exercises
Bibliography and Historical Notes
Chapter 9: Competitive Neural Nets
9.1 The MAXNET
9.1.1 Training a MAXNET
9.1.2 Application of MAXNET
9.2 Kohonen’s Self-organizing Map (SOM)
9.2.1 SOM Architecture
9.2.2 Learning by Kohonen’s SOM
9.2.3 Application
9.3 Learning Vector Quantization (LVQ)
9.3.1 LVQ Learning
9.3.2 Application
9.4 Adaptive Resonance Theory (ART)
9.4.1 The Stability-Plasticity Dilemma
9.4.2 Features of ART Nets
9.4.3 ART 1
Chapter Summary
Solved Problems
Test Your Knowledge
Answers
Exercises
Bibliography and Historical Notes
Chapter 10: Backpropagation
10.1 Multi-layer Feedforward Net
10.1.1 Architecture
10.1.2 Notational Convention
10.1.3 Activation Functions
10.2 The Generalized Delta Rule
10.3 The Backpropagation Algorithm
10.3.1 Choice of Parameters
10.3.2 Application
Chapter Summary
Solved Problems
Test Your Knowledge
Answers
Exercises
Bibliography and Historical Notes
Chapter 11: Elementary Search Techniques
11.1 State Spaces
11.2 State Space Search
11.2.1 Basic Graph Search Algorithm
11.2.2 Informed and Uninformed Search
11.3 Exhaustive Search
11.3.1 Breadth-first Search (BFS)
11.3.2 Depth-first Search (DFS)
11.3.3 Comparison Between BFS and DFS
11.3.4 Depth-first Iterative Deepening
11.3.5 Bidirectional Search
11.3.6 Comparison of Basic Uninformed Search Strategies
11.4 Heuristic Search
11.4.1 Best-first Search
11.4.2 Generalized State Space Search
11.4.3 Hill Climbing
11.4.4 The A/A* Algorithms
11.4.5 Problem Reduction
11.4.6 Means-ends Analysis
11.4.7 Mini-Max Search
11.4.8 Constraint Satisfaction
11.4.9 Measures of Search
11.5 Production Systems
Chapter Summary
Solved Problems
Test Your Knowledge
Answers
Exercises
Bibliography and Historical Notes
Chapter 12: Advanced Search Strategies
12.1 Natural Evolution: A Brief Review
12.1.1 Chromosomes
12.1.2 Natural Selection
12.1.3 Crossover
12.1.4 Mutation
12.2 Genetic Algorithms (GAs)
12.2.1 Chromosomes
12.2.2 Fitness Function
12.2.3 Population
12.2.4 GA Operators
12.2.5 Elitism
12.2.6 GA Parameters
12.2.7 Convergence
12.3 Multi-objective Genetic Algorithms
12.3.1 MOO Problem Formulation
12.3.2 The Pareto-optimal Front
12.3.3 Pareto-optimal Ranking
12.3.4 Multi-objective Fitness
12.3.5 Multi-objective GA Process
12.4 Simulated Annealing
Chapter Summary
Solved Problems
Test Your Knowledge
Answers
Exercises
Bibliography and Historical Notes
Chapter 13: Hybrid Systems
13.1 Neuro-genetic Systems
13.1.1 GA-based Weight Determination of Multi-layer Feed-forward Net
13.1.2 Neuro-evolution of Augmenting Topologies (NEAT)
13.2 Fuzzy-neural Systems
13.2.1 Fuzzy Neurons
13.2.2 Adaptive Neuro-fuzzy Inference System (ANFIS)
13.3 Fuzzy-genetic Systems
Chapter Summary
Test Your Knowledge
Answers
Bibliography and Historical Notes
Acknowledgements
Copyright
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