Contents

1. Introduction to Soft Computing

1. Neural Networks

1.1 Advantages of Neural Networks

1.2 Applications of Neural Network

1.3 Neural Networks in Character Recognition

1.3 Scope of Neural Network

2. Fuzzy Logic: Definition, Applications

3. Genetic Algorithms: Definition, Applications

2. Neural Network

1. Introduction

1.1 Historical Background of Neural Network

2. Fundamental Concepts

2.1 Hybrid Intelligent Systems

2.2 Biological Neurons

2.3 Brain Vs Computers

3. Artificial Neurons, Neural Networks and Architectures

3.1 Neuron Abstraction

3.2 Neuron Activation 15

3.3 Neuron Signal Functions

3.4 Mathematical Preliminaries

3.5 Neural Networks

3.6 Network Architecture

3.7 Salient Properties of Neural Networks

4. Geometry of Binary Threshold Neurons and their Networks

4.1 Pattern Recognition and Data Classification

4.2 Convex Sets, Convex Hulls and Linear Separability

4.3 Space of Boolean Functions

4.4 Binary Neurons are a Pattern Dichotomizers

4.5 Non-linearly Separable Problems

4.6 Capacity of a Simple Threshold Logic Neuron

4.7 Revisiting XOR Problem

4.8 Multilayer Networks

4.9 How Many Hidden Nodes are enough?

5. Learning and Memory

5.1 An Anecodatal Introduction

5.2 The Behavioral Approach to Learning

5.3 The Molecular Problem of Memory

5.4 Learning Algorithms

5.5 Error Correction and Gradient Descent Rules

5.6 The Learning Objectives of TLNs

5.7 Learning Objective

5.8 Pattern Space and Weight Space

6. Linear Separability, Hebb Network, Perceptron Network

6.1 Linear Separability

6.2 Hebb Network

6.3 Perceptron Network

6.4 Learning (Training) Process

6.5 Design in Weight Space

6.6 ?-Least Mean Square Learning

6.7 ?–LMS Works with Normalized Training Patterns

7. MSE Error Surface and its Geometry

7.1 Steepest Descent Search with Exact Gradient Information

7.2 ?-LMS Approximate Gradient Descent

7.3 ?-LMS Algorithm: Convergence in the Mean

8. Application of LMS to Noise Cancellation

3. Fuzzy Set Theory

1. Brief Review of Conventional Set Theory

1.1 Definition of Set

1.2 Set Terminologies

1.3 Operations of Classical Sets

1.4 Properties of Classical Sets

1.5 Mapping of Classical Sets to Functions

2. Fuzzy Sets

2.1  Fuzzy Set as a Whole

2.2 Fuzzy Set Terminologies

2.3  Fuzzy Set Operations

2.4 Properties of Fuzzy Sets

3. Cartesian Product

4. Crisp Relations

5. Fuzzy Relations

6. Tolerance and Equivalence Relations

7. Fuzzy Tolerance and Equivalence Relations

7.1 Fuzzy Equivalence Relation

7.2 Fuzzy Tolerance Relation

8. Value Assignments

9. Membership Functions

9.1 Features of Membership Functions

10. Various Forms

10.1 Standard Forms and Boundaries

11.  Fuzzification

11.1  Fuzzification Process

12. Defuzzification to Crisp Set

13. ?-Cuts for Fuzzy Relations

14. Defuzzification to Scalars

14.1  Defuzzification Methods

15. Fuzzy Logic 102

15.1 What is Fuzzy Logic?

15.2 Fuzzy Propositions

15.3 Logical Connectives for Fuzzy Logic

16.  Approximate Reasoning

17.  Other Forms of Implication Operation

18. Natural Language

19. Linguistic Hedges

19.1 Linguistic Variables

20.  Fuzzy (Rule Based) System

20.1 Graphical Technique of Interference

20.2 Fuzzy Inference Process

20.3  Structure of Fuzzy Inference System

21. Graphical Techniques of Inference

21.1 Comparison between Mamdani and Sugeno model

22. Membership Value Assignments

23. Inference

4. Genetic Algorithms

1. Introduction

1.1 History of Genetic Algorithms

2. What is Genetic Algorithm?

3. Why Genetic Algorithm?

3.1 Application of GA

4. Robustance of Traditional Optimization and Search Methods

4.1 Traditional Optimization or Search Methods

5.  Goals of Optimization

6. How are Genetic Algorithms Different from Traditional Methods?

6.1 Basic Terminologies in GA

7. Simple GA

7.1 Encoding Methods in Genetic Algorithm

7.2 Selection

7.3 Operators in Genetic Algorithm

7.4 Search Termination / Termination Condition

8. Genetic Algorithms At Work – A Simulation By Hand

9. Grist for the Search Mill – Important Similarities

10. Similarity Templates (Schemata)

11. Learning the Lingo