Fuzzy Logic for Business, Finance, and Management (Advances in Fuzzy Systems U Applications and Theory) (Advances in Fuzzy Systems - Applications and Theory)

253 Pages·2007·0.71 MB·English

by  George Bojadziev

TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
Advances in Fuzzy Systems - Applications and Theory - Vol. 23
Fuzzy Logic
for Business,
Finance, and
Management
2nd Edition
George Bojadziev
Simon Fraser University, Canada
Maria Bojadziev
British Columbia Institute of Technology, Canada
World Scientific
NEW JERSEY . LONDON . SINGAPORE . BEIJING . SHANGHAI . HONG KONG . TAIPEI . CHENNAI
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World Scientific Publishing Co. Pte. Ltd.
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British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Advances in Fuzzy Systems: Applications and Theory — Vol. 23
FUZZY LOGIC FOR BUSINESS, FINANCE, AND MANAGEMENT
(2nd Edition)
Copyright © 2007 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
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For photocopying of material in this volume, please pay a copying fee through the Copyright
Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to
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ISBN-13 978-981-270-649-2
ISBN-10 981-270-649-6
Printed in Singapore.
Steven - Fuzzy Logic.pmd 1 3/9/2007, 11:09 AM
To our dear children
Luba and Nick
and
to our beloved grandchildren
Lara-Maria and Nicole-Ann.
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Contents
Foreword xi
PrefacetotheSecondEdition xiii
PrefacetotheFirstEdition xv
ListofCaseStudies xix
1 Fuzzy Sets 1
1.1 Classical Sets: Relations and Functions . . . . . . . . . 1
1.2 De(cid:12)nition 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 Modi(cid:12)ers . . . . . . . . . . . . . . . . . . . . 46
2.6 Composition Rules for Fuzzy Propositions . . . . . . . . 50
2.7 Semantic Entailment . . . . . . . . . . . . . . . . . . . . 54
2.8 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
vii
viii Contents
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 DecisionMakingbyIntersectionofFuzzyGoalsandCon-
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 (Con(cid:13)ict Resolution) . . . . . . . . . . . . . 138
5.6 Defuzzi(cid:12)cation . . . . . . . . . . . . . . . . . . . . . . . 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
Contents ix
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