Belief Functions in Business Decisions

356 Pages·2002·15.463 MB·English

by  Rajendra P. Srivastava, Theodore J. Mock (auth.), Professor Rajendra P. Srivastava, Professor Theodore J. Mock (eds.)

H.-N. Teodorescu, LC. .Jain, A. Kandel (Eds.) W.Liu
Hardware Implementation of Propositional, Probabilistic and
Intelligent Systems Evidential Reasoning
The book offers an ovuview of a large spec Inl~raling Numerical and Symbolic Apploa<lles
trum of implementations for the computa The book systematically provides the reader
tional intelligence based on neuro_fuzzy and
with a broad range of systems/research work
artificial approachu. The clear and concise
to date tllat addresses the importance of com
explanations help the reader to understand
hining numerical and symbolic approaches to
the hardware implementation as~cts of the reasoning under uncertainty in complex
new computational intelligence paradigms.
applications.
2001. XIII. 282 pp. lOS figs.6 tabs. (Vol, 74) Hardcover 2001, XIV, 274 pp. 9 fig<. 3S tabs. (Voj, 7n Hmkover
€ 59.95; sFr 99,50 IS8N 3-7908-1399-0 € 59,95; sFr 99.50 tSBN 3-7908-1414-8
V. Lola, S. Sessa (Eds.) U. Selffen, L.C.Jain (Eds.)
Soft Computing Agents Self-Organizing Neural Networks
New Trends for Designing Autonomous Systems R~~t Advan(es and Appli(alion~
The book is devoted to a unifying ~rs~ctive H is a compact and vivid coll«tion of almost
of this topic. Fundamental topics explored in all aspects of current research on Self-Orga
this volume are: -soft·computing approaches niting Map~, ranging from theoretical work,
to define distributed problem_solving tech numerical and implementation details On
niques to represent and reaSOn about large sequential and parallel hardware to
scale control systems; -t'nrichmt'nt of agent self-organisation with spiking neurons.
programming paradigm for coo~rative soft 2002, XtV.278 pp. 119[ogs_ 27 tab. . Nol, 78) Hard
computing processing.
cOW'r € 59,95; sFr99,50 tSBN 3-7908-1417·2
2001.VlII, 220 pp.S2 rtg<. 13 tabs. (Vol. 75) Hardcovel
€ 54,95:>I'r 91.-tS8N 3-7908-1404-0
Yoo wiU (,rod mor~ inform.otio<>:
Please order from
Springer' Customer 5trvi(e www.springer_de/studiesfuzziness
Habentr.7
t
69126 Heidelberg, Germany
Tel.: +49 (D) 6221-34S-217/8
Fax: +49 {OJ 6221-345-229
e-mail: [email protected]
Of tllrougll your bookseller Springer
AU p, .....' . nor-p,i<" ,ub;o<t to local VAT, ••"g i,, i"n" G', etm.ny ~ VAT for booIu.
Pric. ..n d 0,1\" d. ..i ls .r< >ubi«' '0 <h.",. _i«. d&p' BA ~
Belief Functions in Business Decisions
Studies in Fuzziness and Soft Cornputing
Editor-in-chief
Prof. Janusz Kacprzyk
Systems Research Institute
Po1ish Academy of Sciences
ul. Newe1ska 6
01-447 Warsaw, Po1and
E-mail: [email protected]
http://www.springer.de/cgi-bin/search_book.p1?series=2941
Further volumes of this series can Vol. 77. W. Liu
be fouod at our homepage. Propositional, Probabilistic and Evidential
Reasoning, 2001
ISBN 3-7908-1414-8
Vol. 66. R J. Howlett and L. C. Jain (Eds.)
Radial Basis Function Networks 1, 2001 Vol. 78. U. Seiffert and L. C. Jain (Eds.)
ISBN 3-7908-1367-2 Se/f-Organizing Neural Networks, 2002
ISBN 3-7908-1417-2
Vol. 67. RJ. Howlett and L.c. Jain (Eds.)
Radial Basis Function Networks 2, 2001 Vol. 79. A. Osyczka
ISBN 3-7908-1368-0 Evolutionary Algorithms for Single and
Multieriteria Design Optimization, 2002
Vol. 68. A. Kandel, M. Last and H. Bunke (Eds.) ISBN 3-7908-1418-0
Data Mining and Computational Intelligence, 2001
Vol. 80. P. Wong, F. Aminzadeh and M. Nikravesh
ISBN 3-7908-1371-0
(Eds.)
Soft Computing for Reservoir Charaeterization
Vol. 69. A. Piegat
and Modeling, 2002
Fuzzy Modeling and Contral, 2001
ISBN 3-7908-1421-0
ISBN 3-7908-1385-0
Vol. 81. V. Dimitrov and V. Korotkich (Eds.)
Vol. 70. W. Pedrycz (Ed.) Fuzzy Logic, 2002
Granular Computing, 2001 ISBN 3-7908-1425-3
ISBN 3-7908-1387-7
Vol. 82. Ch. Carlsson and R Fuller
Vol. 71. K. Leiviskä (Ed.) Fuz...ry Reasoning in Decision Making and
Industrial Applications of Soft Computing, 2001 Optimization, 2002
ISBN 3-7908-1388-5 ISBN 3-7908-1428-8
Vol. 72. M. Mates Vol. 83. S. Balfo and R. Marin (Eds.)
Fuzzy Cooperative Games, 2001 Fuzzy Logic in Medicine, 2002
ISBN 3-7908-1392-3 ISBN 3-7908-1429-6
Vol. 73. Y. Yoshida (Ed.) Vol. 84. L. C. Jain and J. Kacprzyk (Eds.)
Dynamical Aspects in Fuuy Decision, 2001 New Leaming Paradigms in Soft Computing, 2002
ISBN 3-7908-1397-4 ISBN 3-7908-1436-9
Vol. 74. H.-N. Teodorescu, L.c. Jain and Vol. 85. D. Rutkowska
Neuro-Fuuy Arehitectures and Hybrid Leaming,
A. Kandel (Eds.)
2002
Hardware 1mplementation of Intelligent Systems,
ISBN 3-7908-1438-5
2001
ISBN 3-7908-1399-0 Vol. 86. M. B. Gorzalczany
Computational Intelligenee Systems
Vol. 75. V. Loia and S. Sessa (Eds.) and Applieations, 2002
Soft Computing Agents, 2001 ISBN 3-7908-1439-3
ISBN 3-7908-1404-0
Vol. 87. C. Bertoluzza, M.A. Gi! and D.A. Ralescu
Vol. 76. D. Ruan, J. Kacprzyk and M. Fedrizzi (Eds.) (Eds.)
Soft Computingfor Risk Evaluation and Management, Statistical Modeling, Analysis and Management
2001 of Fuzzy Data, 2002
ISBN 3-7908-1406-7 ISBN 3-7908-1440-7
Rajendra P. Srivastava
Theodore J. Mock
Editors
Belief Functions
in Business Decisions
With 23 Figures
and 57 Tables
Springer-Verlag Berlin Heidelberg GmbH
Professor Rajendra P. Srivastava
Ernst & Young Professor and Director
Ernst & Young Center for Auditing Research and Advanced Technology
The University of Kansas
School of Business
1300 Sunnyside Avenue
Lawrence, KS 66045
USA
[email protected]
Professor Theodore J. Mock
Arthur Andersen Alumni Professor
University of Southern California
Laventhai School of Accounting
Los Angeles, CA 90089
USA
[email protected]
ISSN 1434-9922
ISBN 978-3-7908-2503-9 ISBN 978-3-7908-1798-0 (eBook)
DOI 10.1007/978-3-7908-1798-0
Cataloging-in-Publication Data applied for
Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Belief functions in business decisions: with 57 tables I Rajendra P. Srivastava; Theodore J. Mock, ed. -
Heidelberg; New York: Physica-Verl., 2002
(Studies in fuzziness and soft computing; Vol. 88)
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is
concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting,
reproduction on microfilm or in any other way, and storage in data banks. Duplieation of this publieation
or parts thereof is permitted only under the provisions of the German Copyright Law of September 9,
1965, in its current version, Viola-
tions are liable for prosecution under the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 2002
Originally publisbed by Pbysica-Verlag Heidelberg in 2002
Softcover reprint of the hardcover 1st edition 2002
The use of general descriptive names, registered names, trademarks, ete. in this publieation does not imply,
even in the absence of a specific statement, that such names are exempt from the relevant proteetive laws
and regulations and therefore free for general use.
Hardcover Design: Brich Kirchner, Heidelberg
Preface
We are pleased to edit the book "Belief Functions in Business Decisions." The
purpose of this book is to compile research being conducted in the area of
business decisions using belief functions. The book is published as a volume
under (he series "Studies in Fuzziness and Soft Computing" by Physica-Verlag (A
Springer-Verlag Company). We wish to thank the publisher, and in particular
Professor J. Kacprzyk, Consulting Editor, for his encouragement and support.
We were very fortunate to have an enthusiastic response to our call for papers for
this volume and sincerely thank our authors for their contributions. This book
would not have become a reality if it were not for their contributions.
The diverse nature of belief functions applications to business decisions posed a
challenge for us to find reviewer's for the contributed articles. We sincerely
appreciate the efforts by the reviewers in providing constructive and timely
criticism of the papers. In particular, we would like to thank and acknowledge the
valuable help provided by the following reviewers: Keith Harrison, J-Y. Jaffray,
Juerg Kohlas, Philippe Smets, and Prakash Shenoy. Finally, we would like to
thank our families, in particular our wives, Madhuri Srivastava and Mary Jo
Mock, for their understanding and support during the compilation process.
This book is divided into three parts. The first part deals with the foundations of
belief functions and contains three chapters. The first chapter discusses the basics
of belief functions and is contributed by the editors. The main objective of this
chapter is to introduce the intuitive and conccptual aspects of belief functions. It
also provides examples of applications of belief functions in the auditing domain.
One important observation is that uncertainty encountered in audit evidence is
modeled more conveniently in belief functions than in the probability framework.
This chapter complements the paper by Philippe Smets presented in Chapter 2.
Smets has done a superb job in providing a comprehensive treatment of belief
functions from its historical developments to its various interpretations. He also
discusses how one can make decisions under the belief-function framework in the
traditional sense of maximizing utilities. He i11ustrates this process for two
interpretations of belief functions: the transferable belief function model (TBM)
and upper and lower probabilities. The third chapter "Empirical Models for the
Dempster-Shafer Theory" by M. A. Klopotek, S. T. Wierzchon investigates three
different interpretations of belief functions: the marginally correct approximation,
the qualitative model, and the quantitative model. Another unique feature of their
prescntation is that they use rough set theory and structured query language (SQL)
to express the semantics of belief functions. This chapter will be especially useful
if one is interested in managing uncertainties in databases.
VI
Part 2 on "Systems and Auditing Applications" contains four chapters. The first
chapter on "The Descriptive Ability ofModels of Audit Risk" is contributed by G.
Monroe and J. Ng. The audit risk model is used by the AICPA (American Institute
of Certified Public Accountants) in the United States of America and by
accounting professionals in other countries to plan the audit of the fmancial
statements of a company. In this chapter the authors discuss their empirical
findings where auditors are asked to make judgment about audit risk using their
intuition and compare tbis with the value generated by various models.
Interestingly, their findings indicate that there is no statistical difference between
the auditor's intuitive assessments and the values generated by the belief function
model.
The second chapter eompares the effectiveness and efficieney of audit proeedures
using three different approaches. Here, M. K. P. Jung and H. E. Fink report the
results of simulation experiments of determining audit risk in eomplex situations.
They find that the "belief based audit is always more efficient than a simple one
and can be less efficient than the traditional approach." They also contend that the
belief-based approach is the most effective among the three models used.
K. Harrison, R. Srivastaya, and D. Plumlee contribute the third chapter, wbich
deals with auditors' asse'ssment of the strength of audit evidence. Importantly,
they find that a statistically significant percentage of the auditors represented their
estimates in ways that were consistent with belief functions and were ineonsistent
with Bayesian probabilities.
Peter Gillett contributes chapter 4 of this part. His paper deals with concepts of
conflict and nonspecificity under belief funetions. He contends, "assessing this
conflict can be important for the strategie choices of whether to seek additional
evidence or to discount or retract existing evidenee, and which beliefs to retract."
He further contends: "it is important to eonsider not just the external confliet
between beliefs, but the internal confliet within belief functions arising from
masses assigned to non-intersecting foeal elements." He diseusses six measures of
conflict: two that apply only to separable belief functions, and that require the
canonieal deeomposition to be found, and four based on extensions of the entropy
eoneept. FinaIly, he diseusses a method for using conflict to deeide which of a set
ofbeliefs to retract (or discount). He uses a missile defense context to illustrate the
eoncepts.
The third part of the book deals with applieation of belief functions to operations
management, finance and economies. This part has five chapters. The first chapter
illustrates an example of evidential reasoning in a merger and aequisition decision
when uneertainties are represented in terms of belief functions. In the paper,
Srivastava and Datta take an expert system approach of evidential reasoning
where the network of evidenee, variables, and their interrelationships are obtained
VII
from an expert. This is the fIrst application of belief functions in the area of
mergers and acquisitions. R. Jirousek, J. Vejnarova, and J. Gemela describe a new
way of defining possibilistic belief networks as a sequence of low-dirnensional
distributions connected by operators of composition. In order to make this
approach more comprehensible, they introduce an extended motivation part
explaining the basic notions through a simple example. They conc1ude the paper
by providing a detailed example of an application of the apparatus for financial
analysis of engineering enterprises. The third chapter by P. McBumey and S.
Parsons deals with using belief functions to fore cast demand for mobile satellite
services. They contend that forecasting demand for a new product or service is
always diffIcult and it is even more diffIcult when the product category itself is
new and unfarniliar to potential consumers. Also, the unknown nature of the
impact of technology on product quality and service quality makes it even more
difficult to forecast demand. They fInd that belief functions provide a means of
representing and combining varied beliefs for forecasting demand, which is more
expressive than traditionaJ point prob ability estimates.
Chapter 4 of Part 3 on "Modeling Financial Portfolios Using belief Functions" is
contributed by C. Shenoy and S. Shenoy. The main objective of their paper is to
demonstrate how the theory of belief functions can be used to model financial
portfolios. In particular, they show how to model portfolio changes as new
information becomes available about different factors that influence individual
stocks or a portfolio. Finally, Don Lien provides an application ofbelieffunctions
in econornics. He discusses the relationship between Knightian uncertainty and
belief functions and provides an illustration of a futures hedging decision under
Knightian uncertainty.
Rajendra Srivastava, Lawrence, Kansas
Theodore J. Mock, Rancho Palos Verdes, Califomia
Contents
Preface ................................................... v
Part 1. Foundations
Introduction to BeliefFunctions ............................. .
R. P. Srivastava and T J. Mock
Decision Making in a Context where Uncertainty is
Represented by Belief Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 17
P. Smets
Empirical Models for the Dempster-Shafer Theory . . . . . . . . . . . . . . .. 62
M A. Klopotek and S. T WierzchOil
Part 2. Systems and Auditing Applications
The Descriptive Ability ofModels of Audit Risk. ............... 113
G. Monroe and J Ng
The Effectiveness and Efficiency ofBeliefBased Audit Procedures .. 139
M K. P. Jung and H. E. Fink
Auditors' Evaluations ofUncertain Audit Evidence:
BeliefFunctions versus Probabilities. . . . . .. .................. 161
K. Harrison, R. P. Srivastava and R. D. Plumlee
Conflict, Consistency and Consonance in Belief Funetions:
Coherence and Integrity of Belief Systems. . . . . . . . . . . . . . . . . . . . . 184
P. Gillett
Part 3. Operations Management, Finance and Economics
Applications
Evaluating Mergers and Acquisitions: A Belief Function Approach.. 222
R. P. Srivastava and D. Datta
x
Possibilistic BeliefNetwork Constmcted by Operators of
Composition and Its Application to Financial Analysis. . . . . . . . . . 252
R. Jirousek, J. Vejnarowi and J. Gemela
Using Belief Functions to Forecast Demand for Mobile
Satellite Services. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
P. McBurney and S. Parsons
Modeling Financial Portfolios U sing Belief Functions. . . . . . . . . . .. 316
C. Shenoy and P. Shenoy
Futures Hedging under Prospect Utility and Knightian Uncertainty .. 333
D. Lien