Fuzzy Logic with Engineering Applications

About the Author xi
 
Preface to the Fourth Edition xiii
 
1 Introduction 1
 
The Case for Imprecision 2
 
A Historical Perspective 4
 
The Utility of Fuzzy Systems 7
 
Limitations of Fuzzy Systems 9
 
The Illusion: Ignoring Uncertainty and Accuracy 11
 
Uncertainty and Information 13
 
Fuzzy Sets and Membership 14
 
Chance versus Fuzziness 17
 
Intuition of Uncertainty: Fuzzy versus Probability 19
 
Sets as Points in Hypercubes 21
 
Summary 23
 
References 23
 
Problems 24
 
2 Classical Sets and Fuzzy Sets 27
 
Classical Sets 28
 
Fuzzy Sets 36
 
Summary 45
 
References 46
 
Problems 46
 
3 Classical Relations and Fuzzy Relations 51
 
Cartesian Product 52
 
Crisp Relations 53
 
Fuzzy Relations 58
 
Tolerance and Equivalence Relations 67
 
Fuzzy Tolerance and Equivalence Relations 70
 
Value Assignments 72
 
Other Forms of the Composition Operation 76
 
Summary 77
 
References 77
 
Problems 77
 
4 Properties of Membership Functions, Fuzzification, and Defuzzification 84
 
Features of the Membership Function 85
 
Various Forms 87
 
Fuzzification 88
 
Defuzzification to Crisp Sets 90
 
lambda-Cuts for Fuzzy Relations 92
 
Defuzzification to Scalars 93
 
Summary 102
 
References 103
 
Problems 104
 
5 Logic and Fuzzy Systems 107
 
Part I: Logic 107
 
Classical Logic 108
 
Fuzzy Logic 122
 
Part II: Fuzzy Systems 132
 
Summary 151
 
References 153
 
Problems 154
 
6 Historical Methods of Developing Membership Functions 163
 
Membership Value Assignments 164
 
Intuition 164
 
Inference 165
 
Rank Ordering 167
 
Neural Networks 168
 
Genetic Algorithms 179
 
Inductive

Timothy J. Ross, University of New Mexico, USA
Dr. Ross is a professor within the Department of Civil Engineering at the University of New Mexico where he teaches courses in structural analysis, structural dynamics and fuzzy logic. He is a registered professional engineer with over 30 years' experience in the fields of computational mechanics, hazard survivability, structural dynamics, structural safety, stochastic processes, risk assessment, and fuzzy systems. He is also the founding Editor-in-Chief of the International Journal, Intelligent and Fuzzy Systems.