BELIEFS ON INDIVIDUAL VARIABLES FROM A SINGLE SOURCE TO BELIEFS ON THE JOINT SPACE UNDER DEMPSTER-SHAFER THEORY - An Algorithm

Rajendra P. Srivastava, Kenneth O. Cogger

Abstract

It is quite common in real world situations to form beliefs under Dempster-Shafer (DS) theory on various variables from a single source. This is true, in particular, in auditing. Also, the judgment about these beliefs is easily made in terms of simple support functions on individual variables. However, for propagating beliefs in a network of variables, one needs to convert these beliefs on individual variables to beliefs on the joint space of the variables pertaining to the single source of evidence. Although there are many possible solutions to the above problem that will yield beliefs on the joint space with the desired marginal beliefs, there is no method that will guarantee that the beliefs are derived from the same source, fully dependent evidence. In this article, we describe such a procedure based on a maximal order decomposition algorithm. The procedure is computationally efficient and is supported by objective chi-square and entropy criteria. While such assignments are not unique, alternative procedures that have been suggested, such as linear programming, are more computationally intensive and result in similar m-value determinations. It should be noted that our maximal order decomposition (i.e., minimum entropy) approach provides m-values on the joint space for fully dependent items of evidence.

References

  1. Akresh, A. D., J. K. Loebbecke, and W. R. Scott, Audit approaches and techniques. Research Opportunities in Auditing: The Second Decade, edited by A. R. Abdelkhalik and Ira Solomon, Sarasota, FL: AAA:13-55, 1988.
  2. Arens, A. A., R. J. Elder, and M. Beasley, Auditing and Assurance Services: An Integrated Approach, Englewood Cliffs, NJ: Prentice-Hall, 2006.
  3. American Institute of Certified Public Accountants, Statement on Auditing Standards, No, 31: Evidential Matter, New York: AICPA, 1980.
  4. American Institute of Certified Public Accountants, Audit Evidence. Statement on Auditing Standards. No. 106. New York, NY: AICPA, 2006.
  5. Dubois , D., and H. Prade, The Principles of Minimum Specificity as a Basis for Evidential Reasoning. Uncertainty in Knowledge-Based Systems (Bouchon B., Yager R. R. eds.), Springer-Verlag, LNCS, Volume No. 286:75-84, 1986.
  6. Dubois , D., and H. Prade, Evidence, Knowledge, and Belief Functions. Internal Journal of Approximate Reasoning, Vol. 6: 295-319, 1992.
  7. Dubois , D., and H. Prade, Focusing versus Updating in Belief Function Theory. Advances in the DempsterShafer Theory of Evidence, (Yager R.R., Kacprzyk J, and Fedrizzi M. eds.), Wiley: 71-95, 1994.
  8. Harrison, K., R. P. Srivastava, and R. D. Plumlee. 2002. Auditors' Evaluations of Uncertain Audit Evidence: Belief Functions versus Probabilities. In Belief Functions in Business Decisions, edited by R. P. Srivastava and T. Mock, Physica-Verlag, Heidelberg, Springer-Verlag Company: 161-183.
  9. Shafer, G., A Mathematical Theory of Evidence, Princeton University Press, 1976.
  10. Shafer , G., and R. P. Srivastava, The bayesian and belieffunction formalisms: A general perspective for auditing. Auditing: A Journal of Practice and Theory 9 (Supplement):110-48, 1990.
  11. Shafer, G., P. P. Shenoy, and R. P. Srivastava. 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:61-84, 1988.
  12. Shenoy , P. P., and G. Shafer. Axioms for probability and belief-function propagation. Uncertainty in Artificial Intelligence 4, edited by R. D. Shachter, T. S. Levitt, L. N. Kanal, and J. F. Lemmer, Amsterdam, NorthHolland: 169-98, 1990.
  13. Srivastava , R. P., Belief Functions and Audit Decisions. Auditors Report, Vol. 17, No. 1: 8-12, Fall 1993.
  14. Srivastava , R. P., The Belief-Function Approach to Aggregating Audit Evidence. International Journal of Intelligent Systems, Vol. 10, No. 3:329-356, March 1995b.
  15. Srivastava , R. P., Dutta, and R. Johns, An Expert System Approach to Audit Planning and Evaluation in the Belief-Function Framework. International Journal of Inteligent Systems in Accounting, Finance and Management, Vol. 5, No. 3, 1996, pp. 165-183.
  16. Srivastava, R. P. and H. Lu, Structural Analysis of Audit Evidence using Belief Functions, Fuzzy Sets and Systems, Vol. 131, Issues No. 1, October: 107-120, 2002.
  17. Srivastava, R. P. and T. Mock, Belief Functions in Business Decisions, Physica-Verlag, Heidelberg, Springer-Verlag Company, 2002.
  18. Srivastava, R. P., and G. Shafer, Belief-Function Formulas for Audit Risk. The Accounting Review, Vol. 67, No. 2:249-283, April 1992.
Download


Paper Citation


in Harvard Style

P. Srivastava R. and O. Cogger K. (2009). BELIEFS ON INDIVIDUAL VARIABLES FROM A SINGLE SOURCE TO BELIEFS ON THE JOINT SPACE UNDER DEMPSTER-SHAFER THEORY - An Algorithm . In Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 1: ICAART, ISBN 978-989-8111-66-1, pages 191-197. DOI: 10.5220/0001654401910197


in Bibtex Style

@conference{icaart09,
author={Rajendra P. Srivastava and Kenneth O. Cogger},
title={BELIEFS ON INDIVIDUAL VARIABLES FROM A SINGLE SOURCE TO BELIEFS ON THE JOINT SPACE UNDER DEMPSTER-SHAFER THEORY - An Algorithm },
booktitle={Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},
year={2009},
pages={191-197},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001654401910197},
isbn={978-989-8111-66-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,
TI - BELIEFS ON INDIVIDUAL VARIABLES FROM A SINGLE SOURCE TO BELIEFS ON THE JOINT SPACE UNDER DEMPSTER-SHAFER THEORY - An Algorithm
SN - 978-989-8111-66-1
AU - P. Srivastava R.
AU - O. Cogger K.
PY - 2009
SP - 191
EP - 197
DO - 10.5220/0001654401910197