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A rigorous explanation of fuzzy systems theory plus a detailed illustration of specific practical applications of the powerful engineering tool they represent. Contains a discussion of cutting-edge technology supplemented by the analysis of several successful applications in the areas of approximate reasoning, fuzzy control and fuzzy analysis. Includes scores of exercises, problems, worked examples, step-by-step solutions and comprehensive references.

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CONTENTS
Foreword = ⅶ
Preface = xi
1 Introduction = 1
 1.1 Fuzzy Systems = 1
 1.2 Mode1ling Vague, Imprecise, and Uncertain Information = 2
 1.3 About this Book = 3
2 Elements of Fuzzy Set Theory = 7
 2.1 Fuzzy Sets : An Elementary Introduction = 7
 2.2 Simple Forms of Representing Fuzzy Sets = 13
 2.3 Basic Operations on Fuzzy Sets = 20
 2.4 The Extension Principle = 28
 2.5 Efficient Operations on Fuzzy Sets = 31
 2.6 Semantics of Fuzzy Sets = 42
  2.6.1 Interpretation of Vague Concepts = 43
  2.6.2 Interpretation of Vague Environments = 47
 2.7 Fuzzy Logic = 56
 2.8 Supplementary Remarks and References = 65
  2.8.1 Historical Development : Fuzzy Systems = 65
  2.8.2 Fuzzy Sets and their Semantics = 68
  2.8.3 The Acquisition of Degrees of Membership = 70
  2.8.4 Fuzzy Logic = 71
  2.8.5 The SOLD System - An Implementation = 73
  2.8.6 Exercises = 77
3 Possibilistic Reasoning = 81
 3.1 Possibility Distributions and Uncertainty Measures = 82
 3.2 Concept of a Focusing Expert System for Possibilistic Data = 91
 3.3 Interpretation of Possibilistic Inference Rules = 106
 3.4 Knowledge Representation and Propagation Using Hypergraphs = 114
 3.5 Logic-based Inference Mechanisms = 129
  3.5.1 Possibilistic Logic = 132
  3.5.2 Truth-functional Logic = 139
 3.6 Supplementary Remarks and References = 142
  3.6.1 Historical Development : Approximate Reasoning = 142
  3.6.2 Possibility Distributions = 144
  3.6.3 Fuzzy Measures = 149
  3.6.4 Extensions of Logic-based Mechanisms of Inference = 151
  3.6.5 POSSINFER - An Implementation = 152
  3.6.6 Exercises = 155
4 Fuzzy Control = 159
 4.1 Knowledge - based versus Classical Models = 160
 4.2 Two Approaches to Fuzzy Control = 164
  4.2.1 The Approach of Mamdani = 165
  4.2.2 The Approach of Takagi and Sugeno = 176
 4.3 On the Design Parameters of Fuzzy Controllers = 181
  4.3.1 Identification of Input and Control Variables = 181
  4.3.2 The Domains of the Input and Control Variables = 181
  4.3.3 Fuzzy Partitions of the Domains = 182
  4.3.4 Linguistic Rules = 182
  4.3.5 Evaluation of Linguistic Rules = 184
  4.3.6 The Choice of the Defuzzification Strategy = 185
  4.3.7 Optimizing a Fuzzy Controller = 185
 4.4 Fuzzy Control as Interpolation in the Presence of Imprecision = 185
  4.4.1 Equality Relations as a Basis for Fuzzy Control = 186
  4.4.2 Interpretation of a Mamdani Controller Based on Equality Relations = 194
 4.5 Fuzzy Control and Relational Equations = 209
 4.6 Supplementary Remarks and References = 216
  4.6.1 Historical Development : Fuzzy Control = 216
  4.6.2 Fuzzy Control = 217
  4.6.3 Realization of Fuzzy Controllers = 218
  4.6.4 Control of the Engine Idle Speed of a Spark Ignition Engine - An Implementation = 222
  4.6.5 Exercises = 233
Symbols = 237
References = 241
Index = 263