Skip to main content
SpringerLink
Log in
Book cover

Belief Functions in Business Decisions pp 1–16Cite as

Introduction to Belief Functions

  • Chapter

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 88))

Abstract

This chapter introduces a theoretical perspective that may be used in business research and practice when confronting decision tasks that involve uncertainly. The main body of the chapter is an introduction to Belief Functions. The introduction includes a discussion of the fundamental constructs and then illustrates the use of belief functions in a business (audit) setting.

The refusal to choose is a form of choice; Disbelief is a form of belief.

-Frank Barron

Based on Srivastava and Mock 2000. Belief Functions in Accounting Behavioral Research. Advances in Accounting Behavioral Research, Vol. 3: 225–242.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • American Institute of Certified Public Accountants. 1983. Statement on Auditing Standards, No, 47: Audit Risk and Materiality in Conducting an Audit. New York: AICPA.

    Google Scholar 

  • American Institute of Certified Public Accountants. 1997a. AICPA/CICA Web Trust Principles and Criteria for Business-to-Consumer Electronic Commerce. http://www.aicpa.org/webtrust/princrit/htm.

  • American Institute of Certified Public Accountants. 1997b. Report of the Special Committee on Assurance Services. http://www.aicpa.org.

  • Curley, S. P., and Golden, J.I. 1994. Using belief functions to represent degrees of belief. Organization Behavior and Human Decision Processes: 271 — 303.

    Google Scholar 

  • Einhorn, H. J., and Hogarth, R. M. 1986. Decision Making under Ambiguity. The Journal of Business, 59(4), Pt. 2 (October), S225 - S250.

    Google Scholar 

  • Gabbay, D. M., and P. Smets. 1998. Handbook of Defeasible Reasoning and Uncertainty Management Systems. Kluwer Academic Publishers.

    Google Scholar 

  • Harrison, K. 1999. Evaluation and Aggregation of Audit Evidence under Uncertainty: An Empirical Study of Belief Functions. Ph.D. Dissertation, School of Business, University of Kansas.

    Google Scholar 

  • Krishnamoorthy, G., T.J. Mock, and M. Washington. 1999. A Comparative Evaluation of Belief Revision Models in Auditing. Auditing: A Journal of Practice and Theory, Vol. 18, pp. 104 - 126.

    Google Scholar 

  • Monroe, G and J. Ng. 2001. The Descriptive Ability of Models of Audit Risk. Belief-Functions in Business Decisions. R. Srivastava and T. Mock (Eds).

    Google Scholar 

  • Shafer, G. 1976. A Mathematical Theory of Evidence Princeton University Press.

    Google Scholar 

  • Shafer, G., and A. Tversky. 1985. Languages and Designs for Probability Judgment. Cognitive Science, vol. 9, pp. 309 - 339.

    Article  Google Scholar 

  • Shafer, G., P.P. Shenoy, and R. P. Srivastava. 1988. Auditor’s Assistant: A knowledge engineering tool for audit decisions. Proceedings of the 1988 Touche Ross/University of Kansas Symposium on Auditing Problems. Lawrence, KS: School of Business, University of Kansas, pp. 61-84.

    Google Scholar 

  • Shafer, G., and R.P. Srivastava. 1990. The bayesian and belief-function formalisms. A general perspective for auditing. Auditing: A Journal of Practice and Theory 9 (Supplement), pp. 110 - 48.

    Google Scholar 

  • Smets, P. 1990a. The Combination of Evidence in the Transferable Belief Model. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12, 5 (May).

    Google Scholar 

  • Smets, P. 1990b. Constructing the Pignistic Probability Function in a Context of Uncertainty. Uncertainty in Artificial Intelligence 5. ed. by Henrion, M., Shachter, R.D., Kanal, L.N., and Lemmer, J.F. North-Holland: Elsevier Science Publishers B. V.

    Google Scholar 

  • Smets, P. 1998. The Transferable Belief Model For Quantified Belief Representation. Quantified Representation for Uncertainty and Imprecision, Vol. 1. Edited by P. Smets. Kluwer Academic Publishers

    Google Scholar 

  • Spohn, W. 1998. Ordinal Conditional functions: A Dynamic Theory of Epistemic States. Causation. Decision, Belief Changes, and Statistics, II, edited by W. L. Harper and B. Skyrms. D. Reidel.

    Google Scholar 

  • Spohn, W. 1990. A General Non-Probabilistic Theory of Inductive Reasoning, Uncertainty in Artificial Intelligence. Elsvier Science Publications: 149 - 158.

    Google Scholar 

  • Srivastava, R. P. 1995a. A General Scheme for Aggregating Evidence in Auditing: Propagation of Beliefs in Networks. Artificial Intelligence in Accounting and Auditing, Vol. 3, Miklos A. Vasarhelyi, editor, Markus Wiener Publishers, Princeton: 55 - 99.

    Google Scholar 

  • Srivastava, R. P. 1995b. The Belief-Function Approach to Aggregating Audit Evidence” International Journal of Intelligent Systems (March): 329-356.

    Google Scholar 

  • Srivastava, R. P. 1996. Value Judgments using Belief Functions. Research in Accounting Ethics, Vol. 2, pp. 109 - 130.

    Google Scholar 

  • Srivastava, R. P. 1997a. Decision Making Under Ambiguity: A Belief-Function Perspective. Archives of Control Sciences, Vol. 6 (XLII): 5 - 27.

    Google Scholar 

  • Srivastava, R. P. 1997b. Integrating Statistical and Non-Statistical Evidence Using Belief Functions. Encyclopedia of Computer Science and Technology, Vol. 37, edited by Allen Kent, James G. Williams, and Carolyn M. Hall, published by Marcel Dekker, Inc., New York (Supplement 22), pp. 157-174.

    Google Scholar 

  • Srivastava, R. P. and G. Shafer. 1992. Belief-Function Formulas for Audit Risk. The Accounting Review, Vol. 67, No. 2 (April): 249 - 283.

    Google Scholar 

  • Srivastava, R. P., and G. Shafer. 1994. Integrating Statistical and Non-Statistical Audit Evidence Using Belief Functions: A Case of Variable Sampling. International Journal of Intelligent Systems, Vol. 9: 519 - 539.

    Article  Google Scholar 

  • Srivastava, R. P., S. Dutta, and R. Johns. 1996. An Expert System Approach to Audit Planning and Evaluation in the Belief-Function Framework. International Journal of Intelligent Systems in Accounting, Finance and Management, Vol. 5, No. 3: 165 - 183.

    Google Scholar 

  • Srivastava, R. P., and T. J. Mock. 1999. Evidential Reasoning for WebTrust Assurance Services. Journal of Management Information Systems. Winter 1999-2000, Vol.1,6, No. 3, pp. 11 — 32. 16

    Google Scholar 

  • Srivastava, R. P. and T. J. Mock. 2000. Belief Functions in Accounting Behavioral Research, Advances in Accounting Behavioral Research, Vol. 3: 225 - 242.

    Article  Google Scholar 

  • Wright, A., T. J. Mock, and R. P. Srivastava. 1998. Audit Program Planning using A Belief Function Framework. Proceedings of the 1998 Deloitte and Touche University of Kansas Symposium on Auditing Problems, Lawrence, KS: School of Business, University of Kansas, pp. 115 - 142.

    Google Scholar 

  • Zadeh, L. A. 1978. Fuzzy sets as a Basis for a Theory of Probability. Fuzzy Sets and Systems, 1: 3 - 28.

    Article  Google Scholar 

  • Zadeh, L. A. 1979. A Theory of Approximate Reasoning. Machine Intelligence, edited by J. E. Ayes, D. Mitchie andn L I Mikulich. Chichester, UK: Ellis Horwood.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Kansas, USA

    Rajendra P. Srivastava

  2. University of Southern California, USA

    Theodore J. Mock

Authors
  1. Rajendra P. Srivastava
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Theodore J. Mock
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Business, Ernst & Young Center for Auditing Research and Advanced Technology, The University of Kansas, 1300 Sunnyside Avenue, 66045, Lawrence, KS, USA

    Rajendra P. Srivastava (Ernst & Young Professor and Director) (Ernst & Young Professor and Director)

  2. Laventhal School of Accounting, University of Southern California, 90089, Los Angeles, CA, USA

    Theodore J. Mock (Arthur Andersen Alumni Professor) (Arthur Andersen Alumni Professor)

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Srivastava, R.P., Mock, T.J. (2002). Introduction to Belief Functions. In: Srivastava, R.P., Mock, T.J. (eds) Belief Functions in Business Decisions. Studies in Fuzziness and Soft Computing, vol 88. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1798-0_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-7908-1798-0_1

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-2503-9

  • Online ISBN: 978-3-7908-1798-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation