Methods of dealing with uncertainty in expert system

Representing uncertainty in expert systems from bhupendra kumar

3. Textbook for a course in expert systems,if an emphasis is placed on Chapters 1 to 3 and on a selection of material from Chapters 4 to 7. There is also the option of using an additional commercially available sheU for a programming project. In assigning a programming project, the instructor may use any part of a great variety of books covering many subjects, such as car repair. Instructions for mostofthe "weekend mechanic" books are close stylisticaUy to expert system rules. Contents Chapter 1 gives an introduction to the subject matter; it briefly presents basic concepts, history, and some perspectives ofexpert systems. Then itpresents the architecture of an expert system and explains the stages of building an expert system. The concept of uncertainty in expert systems and the necessity of deal­ ing with the phenomenon are then presented. The chapter ends with the descrip­ tion of taxonomy ofexpert systems. Chapter 2 focuses on knowledge representation. Four basic ways to repre­ sent knowledge in expert systems are presented: first-order logic, production sys­ tems, semantic nets, and frames. Chapter 3 contains material about knowledge acquisition. Among machine learning techniques, a methodofrule learning from examples is explained in de­ tail. Then problems ofrule-base verification are discussed. In particular, both consistency and completeness oftherule base are presented.

The management of uncertainty in expert systems has usually been left to ad hoc representations and combining rules lacking either a sound theory or clear semantics. However, the aggregation of uncertain information (facts) is a recurrent need in the reasoning process of an expert system. Facts must be aggregated to determine the degree to which the premise of a given rule has been satisfied, to verify the extent to which external constraints have been met, to propagate the amount of uncertainty through the triggering of a given rule, to summarize the findings provided by various rules or knowledge sources or experts, to detect possible inconsistencies among the various sources, and to rank different alternatives or different goals.

There is no uniformly accepted approach to solve this issue. A variety of approaches will be described as part of the review of the state of the art in reasoning with uncertainty. We will examine quantitative and qualitative characterizations of uncertainty. Among the quantitative approaches, we will cover single-valued approaches (Bayes Rule, Modified Bayes Rule, Confirmation Theory); interval-valued approaches (Dempster-Shafer Theory, Probability Bounds, Evidential Reasoning); and fuzzy-valued approaches (Necessity and Possibility Theory). Among the qualitative approaches we will exmine formal (Reasoned Assumptions) and heuristic (Endorsements).

These approaches will then be evaluated according to a list of criteria that reflect a crucial set of requirements common to a large variety of problems.

Keywords

  • Expert System
  • Belief Function
  • Possibility Distribution
  • Possibility Theory
  • Approximate Reasoning

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter

EUR   29.95

Price includes VAT (Singapore)
  • DOI: 10.1007/978-3-642-83991-7_6
  • Chapter length: 20 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Buy Chapter

eBookEUR   106.99Price includes VAT (Singapore)

  • ISBN: 978-3-642-83991-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Buy eBook

Softcover BookEUR   129.99Price excludes VAT (Singapore)

  • ISBN: 978-3-540-51823-5
  • Dispatched in 3 to 5 business days
  • Exclusive offer for individuals only
  • Free shipping worldwide
    Shipping restrictions may apply, check to see if you are impacted.
  • Tax calculation will be finalised during checkout
Buy Softcover Book

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Picro P. Bonissone. Plausible Reasoning: Coping with Uncertainty in Expert Systems. In Stuart Shapiro, Editor, Encyclopedia of Artificial Intelligence, pages 854– 863. John Wiley and Sons Co., New York, 1987.

    Google Scholar 

  2. Picro P. Bonissone. Summarizing and Propagating Uncertain Information with Triangular Norms. International Journal of Approximate Reasoning, 1(1 ):71–101, January 1987.

    CrossRef  MathSciNet  Google Scholar 

  3. Piero P. Bonissone and Richard M. Tong. Editorial: Reasoning with Uncertainty in Expert Systems. International Journal of Man-Machine Studies, 22(3):241–250, 1985.

    Google Scholar 

  4. L.A. Zadeh. Syllogistic reasoning in fuzzy logic and its application to usuality and reasoning with dispositions. IEEE Trans. Systems, Man and Cybernetics, SMC-15:754–765, 1985.

    MathSciNet  Google Scholar 

  5. L.A. Zadeh. Dispositional logic. Appl. Math. Letters, l(l):95–99, 1988.

    CrossRef  MATH  MathSciNet  Google Scholar 

  6. L.A. Zadeh. A computational approach to fuzzy quantifiers in natural language. Computers and Mathematics, 9:149–184, 1983.

    MATH  MathSciNet  Google Scholar 

  7. L.A. Zadeh. A computational theory of disposition. In Proc. 1984 Int. Conf. Computational Linguistics, pages 312–318, 1984.

    CrossRef  Google Scholar 

  8. B. Schweizer and A. Sklar. Associative Functions and Abstract Semi-Groups. Publicationcs Mathematicae Debrecen, 10:69–81, 1963.

    MathSciNet  Google Scholar 

  9. D. Dubois and H. Prade. Criteria Aggregation and Ranking of Alternatives in the Framework of Fuzzy Set Theory. In H.J. Zimmerman, L.A. Zadeh, and B.R. Gaines, Editors, TIMS/Studies in the Management Science, Vol. 20, pages 209–240. Elsevier Science Publishers, 1984.

    Google Scholar 

  10. P. Bonissone and K.Decker. Selecting uncertainty calculi and granularity: An experiment in trading-off precision and complexity. In L. N. Kanaal and J.F. Lemmer, Editors, Uncertainty in Artificial Intelligence. North Holland, Amsterdam, 1986.

    Google Scholar 

  11. L.A. Zadch. Fuzzy logic and approximate reasoning (in memory of Grigor Moisil). Synlhese, 30:407–428, 1975.

    CrossRef  MATH  Google Scholar 

  12. J. Doyle. Methodological SimpliCity in Expert System Construction: The Case of Judgements and Reasoned Assumptions. The AI Magazine, 4(2):39–43, 1983.

    MathSciNet  Google Scholar 

  13. L.A. Zadch. Review of Books: A Mathematical Theory of Evidence. The AI Magazine, 5(3):8l–83, 1984

    Google Scholar 

  14. L.A. Zadeh. A simple view of the dempster-shafer theory of evidence and its implications for the rule of combinations. Technical Report 33, Berkeley Cognitive Science, Institute of Cognitive Science, University of California, Berkeley,, 1985.

    Google Scholar 

  15. A.P. Dempster. Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics, 38:325–339, 1967.

    CrossRef  MATH  MathSciNet  Google Scholar 

  16. J. Pearl. Reverend Bayes on Inference Engines: a Distributed Hierarchical Approach. In Proceedings Second National Conference on Artificial Intelligence, pages 133–136. AAAI, August 1982.

    Google Scholar 

  17. J. Pearl. How to Do with Probabilities What People Say You Can’t. In Proceedings Second Conference on Artificial Intelligence Applications, pages 1–12. IEEE, December 1985.

    Google Scholar 

  18. Judea Pearl. Evidential Reasoning Under Uncertainty. In Howard E. Shrobe, Editor, Exploring Artificial Intelligence, pages 381–418. Morgan Kaufmann, San Mateo, CA, 1988.

    Google Scholar 

  19. R.O. Duda, P.E. Hart, and N.J. Nilsson. Subjective Bayesian methods for rule-based inference systems. In Proc. AFIPS 45, pages 1075–1082, New York, 1976. AE1PS Press.

    Google Scholar 

  20. E.H. Shortliffe and B. Buchanan. A model of inexact reasoning in medicine. Mathematical Bioscicnces, 23:351–379, 1975.

    CrossRef  MathSciNet  Google Scholar 

  21. A.P. Dempster. A generalization of Bayesian inference. J. Roy. Stat. Soc, Ser. B, 30:205–247, 1968.

    MathSciNet  Google Scholar 

  22. G. Shafer. A Mathematical Theory of Evidence. Princeton University Press, Princeton, New Jersey, 1976.

    MATH  Google Scholar 

  23. T.D. Garvey, J.D. Lowrance, and M.A. Fischler. An inference technique for integrating knowledge from disparate sources. In Proc. 7lh. Intern. Joint Conf. on Artificial Intelligence, Vancouver, British Columbia, Canada, 1981.

    Google Scholar 

  24. J. Lowrance and T.D. Garvey. Evidential reasoning: an implementation for multisensor integration. Technical Report Technical Note 307, SRI International, Artificial Intelligence Center, Menlo Park, California, 1983.

    Google Scholar 

  25. J.D. Lowrance, T.D. Garvey, and T.M. Strrat. A framework for evidential-reasoning systems. In Proc. National Conference on Artificial Intelligence, pages 896–903, Menlo Park, California, 1986. AAAI.

    Google Scholar 

  26. J.R. Quinlan. Consistency and Plausible Reasoning. In Proceedings Eight International Joint Conference on Artificial Intelligence, pages 137–144. AAAI, August 1983.

    Google Scholar 

  27. C.R. Rollinger. How to Represent Evidence — Aspects of Uncertainty Reasoning. In Proceedings Eight International Joint Conference on Artificial Intelligence, pages 358–361. AAAI, August 1983.

    Google Scholar 

  28. L.A. Zaclch. Fuzzy sets as a. basis for a theory of possibility. Fuzzy Scts and Systems, 1:3–28, 1978.

    CrossRef  Google Scholar 

  29. L.A. Zadeh. Fuzzy Sets and Information Granularity. In M.M. Gupta, R.K. Ragade, and R.R. Yager, Editors, Advances in Fuzzy Set Theory and Applications, pages 3–18. Elsevier Science Publishers, 1979.

    Google Scholar 

  30. L.A. Zadeh. A theory of approximate reasoning. In P. Hayes, D. Michie, and L.I. Mikulich, Editors, Machine Intelligence, pages 149–194. Halstead Press, New York, 1979.

    Google Scholar 

  31. L.A. Zadeh. Linguistic variables, approximate reasoning, and dispositions. Medical Informatics, 8:173–186, 1983.

    CrossRef  Google Scholar 

  32. R. Reiter. A Logic for Default Reasoning. Journal of Artificial Intelligence, 13:81– 132, 1980.

    CrossRef  MATH  MathSciNet  Google Scholar 

  33. P. Cohen. Heuristic Reasoning about Uncertainty: An Artificial Intelligence Approach. Pittman, Boston, Massachusetts, 1985.

    Google Scholar 

  34. P.R. Cohen and M.R. Grinberg. A Theory of Heuristics Reasoning about Uncertainty. The Al Magazine, pages 17–233, 1983.

    Google Scholar 

  35. P.R. Cohen and M.R. Grinberg. A Framework for Heuristics Reasoning about Uncertainty. In Proceedings Eight International Joint Conference on Artificial Intelligence, pages 355–357. AAAI, August 1983.

    Google Scholar 

  36. E.D. Pednault, S.W. Zucker, and L.V. Muresan. On the Independence Assumption Underlying Subjective Bayesian Updating. Journal of Artificial Intelligence, 16:213– 222, 1981.

    CrossRef  MATH  MathSciNet  Google Scholar 

  37. C. Glymour. Independence Assumptions and Bayesian Updating. Journal of Artificial Intelligence, 25:95–99, 1985.

    CrossRef  MATH  MathSciNet  Google Scholar 

  38. R.W. Johnson. Independence and Bayesian Updating Methods. Journal of Artificial Intelligence, 29:217–222, 1986.

    CrossRef  MATH  Google Scholar 

  39. Yizong Cheng and Rangasami Kashyap. Irrelevancy of evidence caused by independence assumptions. Technical Report TR-EE 86–17, School of Electrical Engineering, Purdue University, West Lafayette, Indiana 47907, 1986.

    Google Scholar 

  40. R. Giles. Semantics for Fuzzy Reasoning. International Journal of Man-Machine Studies, 17(4):401–415, 1982.

    CrossRef  MATH  Google Scholar 

  41. M. Ishizuka, K.S. Fu, aud J.T.P. Yao. Inexact Inference for Rule-Based Damage Assessment of Existing Structure. In Proceedings Seventh International Joint Conference on Artificial Intelligence, pages 1837–842. AAAI, August 1981.

    Google Scholar 

  42. M. Ishizuka. An extension of dempster-shafer theory to fuzzy sets for constructing expert systems. Seisan-Kenkyu, 34:312–315, 1982.

    Google Scholar 

  43. B.C. Buchanan and E.H. Shortlifle. Rule-Based Expert Systems. Addison-Wesley, Reading, Massachusetts, 1984.

    Google Scholar 

  44. D. Heckerman. Probabilistic interpretations for MYCIN certainty factors. In L.N. Kanaal and J.F. Lemmer, Editors, Uncertainty in Artificial Intelligence, pages 167– 196. North-Holland, Amsterdam, 1986.

    Google Scholar 

  45. E. Rich. Default Reasoning as Likelihood Reasoning. In Proceedings Third National Conference on Artificial Intelligence, pages 348–351. AAAI, August 1983.

    Google Scholar 

  46. J.A. Barnett. Computational methods for a mathematical theory of evidence. In Proc. 7th. Intern. Joint Conf on Artificial Intelligence, Vancouver, British Columbia, Canada,, 1981.

    Google Scholar 

  47. T.M. Strat. Continuous belief functions for evidential reasoning. In Proc. National Conference on Artificial Intelligence, pages 308–313, Austin, Texas,, 1984.

    Google Scholar 

  48. D. Dubois and H. Prade. Combination and Propagation of Uncertainty with Belief Functions — A Reexamination. In Proceedings Ninth International Joint Conference on Artificial Intelligence, pa,ges 111–113. AAAI, August 1985.

    Google Scholar 

  49. M.L. Ginsberg. Non-Monotonic Reasoning Using Dempster’s Rule. In Proceedings Fourth National Conference on Artificial Intelligence, pages 126–129. AAAI, August 1984.

    Google Scholar 

  50. P. Smets. The Degree of Belief in a Fuzzy Set. Information Science, 25:1–19, 1981.

    CrossRef  MATH  MathSciNet  Google Scholar 

  51. P. Smcts. Belief functions. In P. Smets, A. Mamdani, D. Dubois, and H. Prade, Editors, Non-Standard Logics for Automated Reasoning. Academic Press, New York, 1988.

    Google Scholar 

  52. L.A. Zadeh. Fuzzy sets. Information and Control, 8:338–353, 1965.

    CrossRef  MATH  MathSciNet  Google Scholar 

  53. H. Prade. A Computational Approach to Approximate Reasoning and Plausible Reasoning with Applications to Expert Systems. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-7(3):260–283, 1985.

    CrossRef  Google Scholar 

  54. Piero P. Bonissone and Allen L. Brown. Expanding the Horizons of Expert Systems. In T. Bernold, Editor, Expert Systems and Knowledge Engineering, pages 267–288. North-Holland, 1986.

    Google Scholar 

  55. Piero P. Bonissone. Using T-norm Based Uncertainty Calculi in a Naval Situation Assessment Application. In Proceedings of the Third AAAI Workshop on Uncertainty in Artificial Intelligence, pages 250–261. AAAI, July 1987.

    Google Scholar 

  56. Piero P. Bonissone and Nancy C Wood. Plausible Reasoning in Dynamic Classification Problems. In Proceedings of the Validation and Testing of Knowledge-Based Systems Workshop. AAAI, August 1988.

    Google Scholar 

  57. Piero P. Bonissone, Stephen Cans, and Keith S. Decker. RUM: A Layered Architecture for Reasoning with Uncertainty. In Proceedings 10th International Joint Conference on Artificial Intelligence, pages 891–898. AAAI, August 1987.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. General Electric Corporate Research and Development, Artificial Intelligence Program, Schenectady, New York, 12301, USA

    Piero P. Bonissone

Authors

  1. Piero P. Bonissone

    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Staatliche Materialprüfungsanstalt (MPA), Universität Stuttgart, Pfaffenwaldring 32, Stuttgart 80, 7000, Germany

    Aleksandar S. Jovanović & Karl F. Kussmaul & 

  2. Institute for Systems Engineering JRC Ispra, Ispra (VA), I-21020, Italy

    Alfredo C. Lucia

  3. General Electric Company, CRD-K-1, 5C32A, Schenectady, NY, 12301, USA

    Piero P. Bonissone

Rights and permissions

Reprints and Permissions

© 1989 Springer-Verlag Berlin, Heidelberg

About this paper

Cite this paper

Bonissone, P.P. (1989). Uncertainty in Kbs (Expert Systems). In: Jovanović, A.S., Kussmaul, K.F., Lucia, A.C., Bonissone, P.P. (eds) Expert Systems in Structural Safety Assessment. Lecture Notes in Engineering, vol 53. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83991-7_6

How expert systems deal with uncertainty?

The management of uncertainty in expert systems has usually been left to ad hoc representations and combining rules lacking either a sound theory or clear semantics. However, the aggregation of uncertain information (facts) is a recurrent need in the reasoning process of an expert system.

What are the 3 techniques in uncertainty reasoning?

We will look at one simple way of handling uncertain answers, and three different methods of dealing with uncertain reasoning: r confidence factors r probabilistic reasoning r fuzzy logic.

What are the various methods to deal with the uncertainty in the knowledge system discuss any one of them?

Research in the expert system domain has provided a variety of methods for dealing with the uncertainty problem. Among them are probability theory, uncertainty theory, the Dempster ISchafer theory, possibility theory, plausibility theory, etc.

What refers to Minimising the global uncertainties of the entire expert system?

Validation refers to minimizing the global uncertainties of the entire expert system.