First Course on Fuzzy Theory and Applications

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Springer Science & Business Media, 2005 - Computers - 335 pages
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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.
  

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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
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Uncertainty Theory
Baoding Liu
No preview available - 2007
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