Advertisement

Introduction to Belief Functions

  • Rajendra P. Srivastava
  • Theodore J. Mock
Part of the Studies in Fuzziness and Soft Computing book series (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.

Keywords

Basic Belief Belief Function Basic Probability Assignment Audit Objective Certified Public Accountant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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
  2. 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.
  3. American Institute of Certified Public Accountants. 1997b. Report of the Special Committee on Assurance Services. http://www.aicpa.org.
  4. 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
  5. 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
  6. Gabbay, D. M., and P. Smets. 1998. Handbook of Defeasible Reasoning and Uncertainty Management Systems. Kluwer Academic Publishers.Google Scholar
  7. 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
  8. 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
  9. 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
  10. Shafer, G. 1976. A Mathematical Theory of Evidence Princeton University Press.Google Scholar
  11. Shafer, G., and A. Tversky. 1985. Languages and Designs for Probability Judgment. Cognitive Science, vol. 9, pp. 309 - 339.CrossRefGoogle Scholar
  12. 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
  13. 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
  14. 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
  15. 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
  16. 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 PublishersGoogle Scholar
  17. 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
  18. Spohn, W. 1990. A General Non-Probabilistic Theory of Inductive Reasoning, Uncertainty in Artificial Intelligence. Elsvier Science Publications: 149 - 158.Google Scholar
  19. 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
  20. Srivastava, R. P. 1995b. The Belief-Function Approach to Aggregating Audit Evidence” International Journal of Intelligent Systems (March): 329-356.Google Scholar
  21. Srivastava, R. P. 1996. Value Judgments using Belief Functions. Research in Accounting Ethics, Vol. 2, pp. 109 - 130.Google Scholar
  22. Srivastava, R. P. 1997a. Decision Making Under Ambiguity: A Belief-Function Perspective. Archives of Control Sciences, Vol. 6 (XLII): 5 - 27.Google Scholar
  23. 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
  24. 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
  25. 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.CrossRefGoogle Scholar
  26. 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
  27. 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. 16Google Scholar
  28. Srivastava, R. P. and T. J. Mock. 2000. Belief Functions in Accounting Behavioral Research, Advances in Accounting Behavioral Research, Vol. 3: 225 - 242.CrossRefGoogle Scholar
  29. 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
  30. Zadeh, L. A. 1978. Fuzzy sets as a Basis for a Theory of Probability. Fuzzy Sets and Systems, 1: 3 - 28.CrossRefGoogle Scholar
  31. 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

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Rajendra P. Srivastava
    • 1
  • Theodore J. Mock
    • 2
  1. 1.University of KansasUSA
  2. 2.University of Southern CaliforniaUSA

Personalised recommendations