Table Of ContentMulticriteria Decision Aid Methods for the
Prediction of Business Failure
Applied Optimization
Volume 12
Series Editors:
Panos M. Pardalos
University 0/ FZorida, U.S.A.
Donald Hearn
University 0/ FZorida, U.S.A.
The titZes published in this series are listed at the end 0/ this voZurne.
Multicriteria Decision
Aid Methods for the
Prediction of
Business Failure
by
Constantin Zopounidis
Technical University ofCrete
and
Augustinos I. Dimitras
Technical University ofCrete
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-1-4419-4787-1 ISBN 978-1-4757-2885-9 (eBook)
DOI 10.1007/978-1-4757-2885-9
Printed on acid-free paper
All Rights Reserved
© 1998 Springer Science+ Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1998
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, e1ectronic or mechanical,
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner.
"Education is the sunfor the learned"
Heraclitus
To our parents
AKNOWLEDGMENTS
We are grateful to Professor P.M. Pardalos for bis great interest to
publish this work in the series "Applied Optimization" as weIl as for bis
encouragement and helpful comments during writing of this work.
Also, we are obliged to M. Doumpos and Tb. Mavridou, both Ph.D.
candidates in Technical University of Crete, for their important notes on an
earlier version and their great help in the preparation of the final manuscript.
TADLE OF CONTENTS
Aknowledgrnents..................................................................................... ix
Table ofContents ................................................................................... xi
List ofTables ......................................................................................... xv
List ofFigures ...................................................................................... , xix
Prologue ............................................................................................ xxi
Chapter I. Business Failure Research: Some Statistics, Methods,
Models and Variables ............................................................ 1
1.1. Introduction .............................................................................. 1
1.2. Methods and models ................................................................. 6
1.2.1. Univariate statistical methods ......................................... 7
1.2.2. Discriminant analysis ..................................................... 8
1.2.3. Linear probability modeL ............................................. 12
1.2.4. Logit and probit analyses .............................................. 13
1.2.5. Recursive partitioning algorithm ................................... 16
1.2.6. SurvivaI Analysis ......................................................... 19
1.2.7. Expert Systems ............................................................. 21
1.2.8. Neural Networks .......................................................... 22
1.3. Financial ratios and other characteristics ................................. 24
1.4. Conclusions ............................................................................ 30
Chapter 11. Multicriteria Decision Aid Methodology ................................ 31
2.1. Introduction ............................................................................ 31
2.2. Multiobjective Mathematical Programming ............................. 33
2.2.1 Multiobjective Mathematical Programming for
bankruptcy prediction ................................................... 34
2.3. Multiattribute Utility Theory .................................................. 38
2.4. Outranking Relations Approach .............................................. 39
2.5. Preference Disaggregation Approach ...................................... 41
2.6. Multicriteria Analysis and Business Failure ............................ 42
Chapter III. ELECTRE TRI Method and Business Failure Prediction ...... 45
3.1. Introduction ............................................................................ 45
3.2. ELECTRE TRI ...................................................................... 46
3.3. The study ofDimitras, Zopounidis and Hurson (1995) ............ 53
3.3.1. Sampie and data ........................................................... 53
xii
3.3.2. Classification Results ................................................... 55
3.4. The study ofDimitras (1995) .................................................. 60
3.4.1. SaIllple and data ........................................................... 60
3.4.2. Classifica.tion Results ................................................... 61
3.4.3. Comparison between ELECTRE TRI and
discriminant analysis .................................................... 66
3.5. Concluding remarks ................................................................ 67
Chapter IV. Rough Sets and Business Failure Prediction .......................... 69
4.1. Introduction ............................................................................ 69
4.1.1. Information table and indiscemibility relation ................ 69
4.1.2. Approximation ofsets ................................................... 70
4.1.3. Reduction and dependency of attributes ......................... 71
4.1.4. Decision roles ............................................................... 72
4.1.5. Decision support using decision roles ............................ 73
4.1.6. Valued closeness relation (VeR) ................................... 74
4.2. The study ofSlowinski and Zopounidis (1995) ........................ 77
4.2.1. SaIllple and data ........................................................... 77
4.2.2. Application ................................................................... 78
4.3. The study of Dimitras, Slowinski, Susmaga, and
Zopounidis (1997) ................................................................. 89
4.3.1. SaIllple and data ........................................................... 89
4.3.2. Applica.tion ................................................................... 89
4.3.3. Comparison of the rough set approach with the
discriminant analysis .................................................... 99
4.3.4. Comparison ofthe rough set approach withthe Iogit
analysis................................................................. . .. .. 103
4.4. The study ofGreco, Matarazzo and Slowinski (1997) ........... 106
4.4.1. SaIllple and data ......................................................... 110
4.4.2 Applica.tion .................................................................. 111
4.5. Concluding remarks .............................................................. 116
Chapter V. Preference Disaggregation Method and Business Failure
Prediction.......................................................................... 117
5.1. Introduction .......................................................................... 117
5.2. The UTA Method ................................................................. 117
5.3. The study ofZopounidis (1987) -The MINORA System ...... 119
5.3.1. Firststep .................................................................... 126
5.3.2. Second Step ................................................................ 129
xiii
5.3.3. Third step ................................................................... 130
5.3.4. Fourth step ................................................................. 131
5.3. The study of Zopounidis and Doumpos (1997) - The
UTADIS method ................................................................... 135
5.3.1. The UTADIS method ................................................. .135
5.3.2. SaInple and data ......................................................... 139
5.3.3. Classification results ................................................... 142
5.3.4. Comparison between UTADIS and Discriminant
Analysis ..................................................................... 143
5.4. Concluding remarks .............................................................. 145
Conclusions .......................................................................................... 147
References ........................................................................................... 151
