S.N. Sivanandam, S. Sumathi and S.N. Deepa

Introduction to FuzzyLogic using MATLAB

With 304 Figures and 37 Tables

&j Springer

Contents

1 Introduction 11.1 Fuzzy Logic 11.2 Mat LAB - An Overview 6

2 Classical Sets and Fuzzy Sets 112.1 Introduction 112.2 Classical Set 11

2.2.1 Operations on Classical Sets 122.2.2 Properties of Classical Sets 142.2.3 Mapping of Classical Sets to a Function 162.2.4 Solved Examples 17

2.3 Fuzzy Sets 192.3.1 Fuzzy Set Operations 202.3.2 Properties of Fuzzy Sets 222.3.3 Solved Examples 23

3 Classical and Fuzzy Relations 373.1 Introduction 373.2 Cartesian Product of Relation 373.3 Classical Relations 38

3.3.1 Cardinality of Crisp Relation 393.3.2 Operations on Crisp Relation 393.3.3 Properties of Crisp Relations 403.3.4 Composition 40

3.4 Fuzzy Relations 413.4.1 Cardinality of Fuzzy Relations 413.4.2 Operations on Fuzzy Relations 423.4.3 Properties of Fuzzy Relations 423.4.4 Fuzzy Cartesian Product and Composition 43

3.5 Tolerance and Equivalence Relations 513.5.1 Crisp Relation 51

XII Contents

3.5.2 Fuzzy Relation 533.5.3 Solved Examples 53

4 Membership Functions 734.1 Introduction 734.2 Features of Membership Function 734.3 Classification of Fuzzy Sets 754.4 Fuzzification 764.5 Membership Value Assignments 76

4.5.1 Intuition 774.5.2 Inference 784.5.3 Rank Ordering 804.5.4 Angular Fuzzy Sets 804.5.5 Neural Networks 814.5.6 Genetic Algorithm 844.5.7 Inductive Reasoning 84

4.6 Solved Examples 85

5 Defuzzification 955.1 Introduction 955.2 Lambda Cuts for Fuzzy Sets 955.3 Lambda Cuts for Fuzzy Relations 965.4 Defuzzification Methods 965.5 Solved Examples 101

6 Fuzzy Rule-Based System 1136.1 Introduction 1136.2 Formation of Rules 1136.3 Decomposition of Rules 1156.4 Aggregation of Fuzzy Rules 1176.5 Properties of Set of Rules 1176.6 Fuzzy Inference System 118

6.6.1 Construction and Working of Inference System 1186.6.2 Fuzzy Inference Methods 1196.6.3 Mamdani's Fuzzy Inference Method 1206.6.4 Takagi-Sugeno Fuzzy Method (TS Method) 1236.6.5 Comparison Between Sugeno and Mamdani Method . . . 1266.6.6 Advantages of Sugeno and Mamdani Method 127

6.7 Solved Examples 127

7 Fuzzy Decision Making 1517.1 Introduction 1517.2 Fuzzy Ordering 1517.3 Individual Decision Making 1537.4 Multi-Person Decision Making 153

Contents XIII

7.5 Multi-Objective Decision Making 1547.6 Fuzzy Bayesian Decision Method 155

Applications of Fuzzy Logic 1578.1 Fuzzy Logic in Power Plants 157

8.1.1 Fuzzy Logic Supervisory Control for Coal Power Plant . 1578.2 Fuzzy Logic Applications in Data Mining 166

8.2.1 Adaptive Fuzzy Partition in Data Base Mining:Application to Olfaction 166

8.3 Fuzzy Logic in Image Processing 1728.3.1 Fuzzy Image Processing 172

8.4 Fuzzy Logic in Biomedicine 2008.4.1 Fuzzy Logic-Based Anesthetic Depth Control 200

8.5 Fuzzy Logic in Industrial and Control Applications 2048.5.1 Fuzzy Logic Enhanced Control of an AC Induction

Motor with a DSP 2048.5.2 Truck Speed Limiter Control by Fuzzy Logic 2108.5.3 Analysis of Environmental Data for Traffic Control

Using Fuzzy Logic 2178.5.4 Optimization of a Water Treatment System Using

Fuzzy Logic 2238.5.5 Fuzzy Logic Applications in Industrial Automation . . . . 2318.5.6 Fuzzy Knowledge-Based System for the Control of a

Refuse Incineration Plant Refuse Incineration 2438.5.7 Application of Fuzzy Control for Optimal Operation

of Complex Chilling Systems 2508.5.8 Fuzzy Logic Control of an Industrial Indexing Motion

Application 2558.6 Fuzzy Logic in Automotive Applications 264

8.6.1 Fuzzy Antilock Brake System 2648.6.2 Antilock-Braking System and Vehicle Speed

Estimation Using Fuzzy Logic 2698.7 Application of Fuzzy Expert System 277

8.7.1 Applications of Hybrid Fuzzy Expert Systems inComputer Networks Design 277

8.7.2 Fuzzy Expert System for Drying Process Control 2888.7.3 A Fuzzy Expert System for Product Life Cycle

Management : 2958.7.4 A Fuzzy Expert System Design for Diagnosis of

Prostate Cancer 3048.7.5 The Validation of a Fuzzy Expert System for Umbilical

Cord Acid-Base Analysis 3098.7.6 A Fuzzy Expert System Architecture Implementing

Onboard Planning and Scheduling for AutonomousSmall Satellite 313

XIV Contents

8.8 Fuzzy Logic Applications in Power Systems 3218.8.1 Introduction to Power System Control 321

8.9 Fuzzy Logic in Control 3438.9.1 Fuzzy Logic Controller 3438.9.2 Automatic Generation Control Using Fuzzy Logic

Controllers 3568.10 Fuzzy Pattern Recognition 359

8.10.1 Multifeature Pattern Recognition 367

9 Fuzzy Logic Projects with Matlab 3699.1 Fuzzy Logic Control of a Switched Reluctance Motor 369

9.1.1 Motor 3709.1.2 Motor Simulation 3709.1.3 Current Reference Setting 3719.1.4 Choice of the Phase to be Fed 373

9.2 Modelling and Fuzzy Control of DC Drive 3759.2.1 Linear Model of DC Drive 3769.2.2 Using PSB to Model the DC Drive 3789.2.3 Fuzzy Controller of DC Drive 3789.2.4 Results 380

9.3 Fuzzy Rules for Automated Sensor Self-Validation andConfidence Measure 3809.3.1 Preparation of Membership Functions 3829.3.2 Fuzzy Rules 3839.3.3 Implementation 384

9.4 FLC of Cart 3879.5 A Simple Fuzzy Excitation Control System (AVR) in Power

System Stability Analysis 3929.5.1 Transient Stability Analysis 3939.5.2 Automatic Voltage Regulator 3939.5.3 Fuzzy Logic Controller Results Applied to a One

Synchronous Machine System 3949.5.4 Fuzzy Logic Controller in an 18 Bus Bar System 396

9.6 A Low Cost Speed Control System of Brushless DC MotorUsing Fuzzy Logic 3989.6.1 Proposed System 3999.6.2 Fuzzy Inference System 4019.6.3 Experimental Result 402

Appendix A Fuzzy Logic in Matlab 409

References 419