Fuzzy Logic: An Introductory Course for Engineering Students

✍ Scribed by Trillas, Enric;Eciolaza, Luka

• Publisher: Springer International Publishing AG
• Year: 2015
• Tongue: English
• Leaves: 211
• Series: Studies in fuzziness and soft computing 320
• Category: Library

✦ Synopsis

This book introduces readers to fundamental concepts in fuzzy logic. It describes the necessary theoretical background and a number of basic mathematical models. Moreover, it makes them familiar with fuzzy control, an important topic in the engineering field. The book offers an unconventional introductory textbook on fuzzy logic, presenting theory together with examples and not always following the typical mathematical style of theorem-corollaries. Primarily intended to support engineers during their university studies, and to spark their curiosity about fuzzy logic and its applications, the book is also suitable for self-study, providing a valuable resource for engineers and professionals who deal with imprecision and non-random uncertainty in real-world applications.

✦ Table of Contents

Preface......Page 7
Contents......Page 9
1.1 A Genesis of Fuzzy Sets......Page 12
1.1.1 L-Degree......Page 14
1.1.2 Fuzzy Sets......Page 16
1.2.1 Antonyms......Page 23
1.2.2 Negations......Page 25
1.2.3 Antonyms and Negations......Page 28
1.2.4 Medium Term......Page 30
1.3.2 OR......Page 31
1.4.1 Qualified Predicates......Page 33
1.4.2 Linguistic Modifiers......Page 34
1.4.3 Constrained Predicates......Page 35
1.4.4 Group Meaning......Page 36
1.4.5 Synonims......Page 37
1.5 Linguistic Variables......Page 39
1.5.1 Fuzzy Partition......Page 40
1.6 A Note on Lattices......Page 42
1.6.1 Examples......Page 44
2.1.1 Cartesian Product......Page 45
2.1.2 Extension Principle......Page 46
2.1.3 Preservation of the Classical Case......Page 47
2.1.4 Resolution......Page 48
2.2.1 Introduction......Page 51
2.2.2 Algebras of Fuzzy Sets......Page 53
2.2.3 Non-contradiction and Excluded-Middle......Page 57
2.2.4 Decomposable Algebras......Page 60
2.2.5 Standard Algebras of Fuzzy Sets......Page 62
2.2.6 Strong Negations......Page 66
2.2.7 Continuous T-Norms and T-Conorms......Page 69
2.2.8 Laws of Fuzzy Sets......Page 71
2.2.9 Examples......Page 78
2.3 On Aggregating Imprecise Information......Page 87
2.3.1 Aggregation Functions......Page 88
2.3.2 Ordered Weighted Means......Page 89
2.3.3 More on Aggregations......Page 90
2.3.4 Examples......Page 91
3.1.1 Logic and Consequence Operators......Page 93
3.1.2 Conjecturing......Page 95
3.2.1 What is a Conditional?......Page 97
3.2.2 The Case of Boolean Algebras......Page 98
3.2.3 Fuzzy Conditionals......Page 100
3.3 Short Note on Other Modes of Reasoning......Page 108
3.4 Inference with Fuzzy Rules......Page 109
3.4.1 Finite Case......Page 112
3.4.2 Inference with Several Rules......Page 113
3.4.3 Examples......Page 116
3.5 Deffuzification......Page 118
3.6 Rules and Conjectures......Page 122
3.7 Two Final Examples......Page 123
4.1 What Is a Fuzzy Relation?......Page 126
4.2 How to Compose Fuzzy Relations?......Page 128
4.3 Which Relevant Properties Do Have a Fuzzy Binary Relation?......Page 130
4.4 The Concept of T-State......Page 133
4.5 Fuzzy relations and α-cuts......Page 134
5.1 Which Is the Aim of This Section?......Page 139
5.2 The Characterization of T-Preorders......Page 141
5.3 The Characterization of T-Indistinguishabilities......Page 142
6.1 Introduction......Page 148
6.2 Fuzzy Numbers......Page 151
6.2.1 Operations with Fuzzy Numbers......Page 152
6.2.2 Operations with Triangular Fuzzy Numbers......Page 153
6.2.3 Note......Page 157
6.3 A Note on the Lattice of Fuzzy Numbers......Page 158
6.3.1 Example......Page 159
6.4 A Note on Fuzzy Quantifiers......Page 161
6.4.1 Quantified Fuzzy Statements......Page 163
7.1 Introduction......Page 166
7.2 The Concept of a Measure......Page 167
7.4 λ-Measures......Page 169
7.5 Measures of Possibility and Necessity......Page 171
7.6 Examples......Page 174
7.7 Probability, Possibility and Necessity......Page 177
7.8 Probability of Fuzzy Sets......Page 178
8.1 Introduction......Page 182
8.2 Revising Conditional and Implications in Fuzzy Control......Page 186
8.2.1 Inference from Imprecise Rules......Page 187
8.2.2 Takagi-Sugeno of Order 1......Page 196
8.3.1 State-Space Representation......Page 197
8.3.2 Takagi-Sugeno Models for Control of Nonlinear Systems......Page 198
8.3.3 Stability Analysis......Page 201
8.3.4 Parallel Distributed Compensation......Page 202
8.3.5 Piecewise Bilinear Model......Page 204
8.3.6 Vertex Placement Principle......Page 206
Bibliography......Page 210