Fuzzy Logic for Business,Finance, and Management

Contents
Foreword xi
Preface to the Second Edition xiii
Preface to the First Edition xv
List of Case Studies xix
1 Fuzzy Sets 1
1.1 Classical Sets: Relations and Functions . . . . . . . . . 1
1.2 Definition of Fuzzy Sets . . . . . . . . . . . . . . . . . . 9
1.3 Basic Operations on Fuzzy Sets . . . . . . . . . . . . . . 15
1.4 Fuzzy Numbers . . . . . . . . . . . . . . . . . . . . . . . 19
1.5 Triangular Fuzzy Numbers . . . . . . . . . . . . . . . . . 22
1.6 Trapezoidal Fuzzy Numbers . . . . . . . . . . . . . . . . 24
1.7 Fuzzy Relations . . . . . . . . . . . . . . . . . . . . . . . 26
1.8 Basic Operations on Fuzzy Relations . . . . . . . . . . . 29
1.9 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2 Fuzzy Logic 37
2.1 Basic Concepts of Classical Logic . . . . . . . . . . . . . 37
2.2 Many-Valued Logic . . . . . . . . . . . . . . . . . . . . . 41
2.3 What is Fuzzy Logic? . . . . . . . . . . . . . . . . . . . 43
2.4 Linguistic Variables . . . . . . . . . . . . . . . . . . . . . 44
2.5 Linguistic Modifiers . . . . . . . . . . . . . . . . . . . . 46
2.6 Composition Rules for Fuzzy Propositions . . . . . . . . 50
2.7 Semantic Entailment . . . . . . . . . . . . . . . . . . . . 54
2.8 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3 Fuzzy Averaging for Forecasting 61
3.1 Statistical Average . . . . . . . . . . . . . . . . . . . . . 61
3.2 Arithmetic Operations with Triangular and Trapezoidal
Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.3 Fuzzy Averaging . . . . . . . . . . . . . . . . . . . . . . 66
3.4 Fuzzy Delphi Method for Forecasting . . . . . . . . . . . 71
3.5 Weighted Fuzzy Delphi Method . . . . . . . . . . . . . . 76
3.6 Fuzzy PERT for Project Management . . . . . . . . . . 77
3.7 Forecasting Demand . . . . . . . . . . . . . . . . . . . . 87
3.8 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4 Decision Making in a Fuzzy Environment 91
4.1 Decision Making by Intersection of Fuzzy Goals and Con-
straints . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.2 Various Applications . . . . . . . . . . . . . . . . . . . . 95
4.3 Pricing Models for New Products . . . . . . . . . . . . . 104
4.4 Fuzzy Averaging for Decision Making . . . . . . . . . . 110
4.5 Multi-Expert Decision Making . . . . . . . . . . . . . . 115
4.6 Fuzzy Zero-Based Budgeting . . . . . . . . . . . . . . . 119
4.7 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5 Fuzzy Logic Control for Business, Finance, and Manage-
ment 127
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 127
5.2 Modeling the Control Variables . . . . . . . . . . . . . . 129
5.3 If . . . and . . . Then Rules . . . . . . . . . . . . . . . . . . 133
5.4 Rule Evaluation . . . . . . . . . . . . . . . . . . . . . . . 136
5.5 Aggregation (Conflict Resolution) . . . . . . . . . . . . . 138
5.6 Defuzzification . . . . . . . . . . . . . . . . . . . . . . . 144
5.7 Use of Singletons to Model Outputs . . . . . . . . . . . 149
5.8 Tuning of Fuzzy Logic Control Models . . . . . . . . . . 150
5.9 One-Input–One-Output Control Model . . . . . . . . . . 152
5.10 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6 Applications of Fuzzy Logic Control 157
6.1 Investment Advisory Models . . . . . . . . . . . . . . . . 157
6.2 Fuzzy Logic Control for Pest Management . . . . . . . . 164
6.3 Inventory Control Models . . . . . . . . . . . . . . . . . 170
6.4 Problem Analysis . . . . . . . . . . . . . . . . . . . . . . 177
6.5 Potential Problem Analysis . . . . . . . . . . . . . . . . 182
6.6 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
7 Fuzzy Queries from Databases: Applications 187
7.1 Standard Relational Databases . . . . . . . . . . . . . . 187
7.2 Fuzzy Queries . . . . . . . . . . . . . . . . . . . . . . . . 190
7.3 Fuzzy Complex Queries . . . . . . . . . . . . . . . . . . 196
7.4 Fuzzy Queries for Small Manufacturing Companies . . . 199
7.5 Fuzzy Queries for Stocks and Funds Databases . . . . . 206
7.6 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
References 217
Index 223


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