ISBN: 3790814474
TITLE: An Introduction to Fuzzy Logic and Fuzzy Sets
AUTHOR: Buckley, Eslami
TOC:

1 Introduction 1
2 Logic 5
2.1 Introduction 5
2.2 Propositional Logic 5
2.2.1 Exercises 10
2.3 Crisp Sets 12
2.3.1 Exercises 15
2.4 Fuzzy Logic 17
2.4.1 Exercises 19
3 Fuzzy Sets 21
3.1 Introduction 21
3.2 Fuzzy Sets 21
3.2.1 Exercises 29
3.3 t-norms, t-conorms 31
3.3.1 Exercises 36
3.4 Algebra of Fuzzy Sets 38
3.4.1 Exercises 40
3.5 Mixed Fuzzy Logic 42
3.5.1 Exercises 44
3.6 Alpha-Cuts 46
3.6.1 Exercises 48
3.7 Distance Between Fuzzy Sets 50
3.7.1 Exercises 52
4 Fuzzy Numbers 55
4.1 Introduction 55
4.2 Fuzzy Numbers 55
4.2.1 Exercises 60
4.3 Fuzzy Arithmetic 63
4.3.1 Extension Principle 63
Exercises 66
4.3.2 Interval Arithmetic 68
Exercises 69
4.3.3 Alfa-Cuts and Interval Arithmetic 71
Exercises 74
4.3.4 Properties of Fuzzy Arithmetic 76
Exercises 78
4.4 Fuzzy Max and Min 79
4.4.1 Exercises 82
4.5 Inequalities 84
4.5.1 Exercises 89
4.6 Defuzzification 91
4.6.1 Exercises 93
5 Fuzzy Equations 95
5.1 Introduction 95
5.2 Linear Equations 95
5.2.1 Classical Solution 96
5.2.2 Extension Principle Solution 97
5.2.3 Alfa-Cut and Interval Arithmetic Solution 99
5.2.4 Exercises 101
5.3 Other Fuzzy Equations 102
5.3.1 Exercises 106
6 Fuzzy Inequalities 109
6.1 Introduction 109
6.2 Solving -^A-^X+-^B\leq-^C 109
6.3 -^A-^X^2+^-B-^X+-^C\geq-^D(or>-^D) 112
6.3.1 Exercises 114
7 Fuzzy Relations 115
7.1 Introduction 115
7.2 Definitions 115
7.2.1 Exercises 120
7.3 Transitive Closure 122
7.3.1 Exercises 126
7.4 Fuzzy Equivalence Relation 129
7.4.1 Exercises 132
7.5 Fuzzy Relation Equations 134
7.5.1 Exercises 138
8 Fuzzy Functions 141
8.1 Introduction 141
8.2 Extension Principle 141
8.2.1 Exercises 147
8.3 Alpha-Cuts and Interval Arithmetic 150
8.3.1 Exercises 153
8.4 Types of Fuzzy Functions 155
8.4.1 Exercises 161
8.5 Inverse Functions 163
8.5.1 Exercises 166
8.6 Derivatives 168
8.6.1 Exercises 173
9 Fuzzy Plane Geometry 175
9.1 Exercises 181
10 Fuzzy Trigonometry 185
10.1 Introduction 185
10.2 Standard Fuzzy Trigonometry 185
10.2.1 Exercises 190
10.3 Hyperbolic Trigonometric Functions 192
10.3.1 Exercises 194
11 Systems of Fuzzy Linear Equations 195
11.1 Exercises 201
12 Possibility Theory 203
12.1 Introduction 203
12.2 Discrete Possibilities 203
12.2.1 Exercises 206
12.3 Fuzzy Markov Chains 208
12.3.1 Exercises 212
13 Neural Nets 215
13.1 Introduction 215
13.2 Layered, Feedforward, Neural Nets 215
13.2.1 Exercises 222
13.3 Fuzzy Neural Nets 224
13.3.1 Exercises 229
14 Approximate Reasoning 231
14.1 Introduction 231
14.2 Approximate Reasoning 231
14.2.1 Exercises 237
14.3 Multiple Rules 240
14.3.1 Exercises 242
14.4 Discrete Case 244
14.4.1 Exercises 248
14.5 Other Methods 249
14.5.1 Exercises 252
15 Genetic Algorithms 253
15.1 Exercises 259
16 Fuzzy Optimization 261
16.1 Introduction 261
16.2 Maximum/Mininimum of Fuzzy Functions 261
16.2.1 Exercises 266
16.3 Fuzzy Problems 268
16.3.1 Exercises 274
Index 277
List of Figures 283
List of Tables 285
END
