# First Course on Fuzzy Theory and Applications

Springer Science & Business Media, 2005 - Computers - 335 pages
Fuzzy theory has become a subject that generates much interest among the courses for graduate students. However, it was not easy to find a suitable textbook to use in the introductory course and to recommend to the students who want to self-study. The main purpose of this book is just to meet that need. The author has given lectures on the fuzzy theory and its applications for ten years and continuously developed lecture notes on the subject. This book is a publication of the modification and summary of the lecture notes. The fundamental idea of the book is to provide basic and concrete concepts of the fuzzy theory and its applications, and thus the author focused on easy illustrations of the basic concepts. There are numerous examples and figures to help readers to understand and also added exercises at the end of each chapter. This book consists of two parts: a theory part and an application part. The first part (theory part) includes chapters from 1 to 8. Chapters 1 and 2 introduce basic concepts of fuzzy sets and operations, and Chapters 3 and 4 deal with the multi-dimensional fuzzy sets. Chapters 5 and 6 are extensions of the fuzzy theory to the number and function, and Chapters 7 and 8 are developments of fuzzy properties on the probability and logic theories.

### What people are saying -Write a review

We haven't found any reviews in the usual places.

### Contents

 Chapter 1 FUZZY SETS 1 12 Operation of Sets 3 13 Characteristics of Crisp Set 5 14 Definition of Fuzzy Set 7 15 Expanding Concepts of Fuzzy Set 14 16 Standard Operation of Fuzzy Set 21 SUMMARY 22 EXERCISES 24
 72 Fuzzy Event 174 73 Uncertainty 179 74 Measure of Fuzziness 181 SUMMARY 189 EXERCISES 190 Chapter 8 FUZZY LOGIC 193 82 Fuzzy Logic 201 83 Linguistic Variable 204

 Chapter 2 THE OPERATION OF FUZZY SET 27 22 Fuzzy Complement 28 23 Fuzzy Union 32 24 Fuzzy Intersection 35 25 Other Operations in Fuzzy Set 38 26 tnorms and tconorms 45 SUMMARY 47 EXERCISES 51 Chapter 3 FUZZY RELATION AND COMPOSITION 53 32 Properties of Relation on A Single Set 62 33 Fuzzy Relation 68 34 Extension of Fuzzy Set 80 SUMMARY 86 EXERCISES 88 Chapter 4 FUZZY GRAPH AND RELATION 91 42 Characteristics of Fuzzy Relation 103 43 Classification of Fuzzy Relation 108 44 Other Fuzzy Relations 116 SUMMARY 124 EXERCISES 126 Chapter 5 FUZZY NUMBER 129 52 Operation of Fuzzy Number 132 53 Triangular Fuzzy Number 137 54 Other Types of Fuzzy Number 145 SUMMARY 149 EXERCISES 150 Chapter 6 FUZZY FUNCTION 153 62 Fuzzy Extrema of Function 158 63 Integration and Differenciation of Fuzzy Function 163 SUMMARY 168 EXERCISES 169 Chapter 7 PROBABILISY AND UNCERTAINTY 171
 84 Fuzzy Truth Qualifier 206 85 Representation of Fuzzy Rule 210 SUMMARY 213 EXERCISES 215 Chapter 9 FUZZY INFERENCE 217 92 Fuzzy Rules and Implication 221 93 Inference Mechanism 224 94 Inference Methods 236 SUMMARY 247 EXERCISES 250 Chapter 10 FUZZY CONTROL AND FUZZY EXPERT SYSTEMS 253 102 Fuzzification Interface Component 255 103 Knowledge Base Component 257 104 Inference Decision Making Logic 265 105 Defuzzification 269 106 Design Procedure of Fuzzy Logic Controller 272 107 Application Example of FLC Design 273 108 Fuzzy Expert Systems 277 SUMMARY 280 EXERCISES 282 Chapter 11 FUSION OF FUZZY SYSTEM AND NEURAL NETWORKS 285 112 Fusion with Neural Networks 290 SUMMARY 306 EXERCISE 308 Chapter 12 FUSION OF FUZZY SYSTEMS AND GENETIC ALGORITHMS 309 122 Fusion with Genetic Algorithms 314 SUMMARY 323 EXERCISE 324 BIBLIOGRAPHY 325 INDEX 333 Copyright