Skip to main content

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 219))

Abstract

We are concerned here with the problem of selecting an optimal alternative in situations in which there exists some uncertainty in our knowledge of the state of the world. We show how the Dempster–Shafer belief structure provides a unifying framework for representing various types of uncertainties. We also show how the OWA aggregation operators provide a unifying framework for decision making under ignorance. In particular we see how these operators provide a formulation of a type epistemic probabilities associated with our degree of optimism.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • A. P. Dempster, “Upper and lower probabilities induced by a multi-valued mapping.” Ann. of Mathematical Statistics, 1967, pp. 325–339.

    Google Scholar 

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

    MATH  Google Scholar 

  • R. R. Yager, “On ordered weighted averaging aggregation operators in multi-criteria decision making.” IEEE Trans. on Systems, Man and Cybernetics, 18, 1988, pp. 83–190.

    Google Scholar 

  • R. R. Yager, “A general approach to decision making with evidential knowledge.” In: Uncertainty in Artificial Intelligence, edited by L. N. Kanal and J. L. Lemmer, North-Holland, Amsterdam, 1986, pp. 317–330.

    Google Scholar 

  • R. R. Yager, “Optimal alternative selection in the face of evidential knowledge.” In: Optimization Models using Fuzzy Sets and Possibility Theory, edited by J. Kacprzyk and S. A. Orlovski, D. Reidel, Dordrecht, 1987, pp. 123–140.

    Google Scholar 

  • S. B. Richmond, Operations Research for Management Decisions, Ronald Press, New York, 1968.

    Google Scholar 

  • M. J. Bolanos, M. T. Lamata and S. Moral, “Decision making problems in a general environment.” Fuzzy Sets and Systems, 25, 1988, pp. 135–144.

    Article  MATH  MathSciNet  Google Scholar 

  • D. Dubois and H. Prade, “Evidence measures based on fuzzy information.” Automatica, 21, 1985, pp. 547–562.

    Article  MATH  MathSciNet  Google Scholar 

  • J. Y. Jaffray, “Application of linear utility theory to belief functions.” In: Uncertainty and Intelligent Systems, edited by B. Bouchon, L. Saitta and R. R. Yager, Springer-Verlag, Berlin, 1988, pp. 1–8.

    Google Scholar 

  • T. M. Strat, “Making decisions with belief functions.” Proceedings Fifth Workshop on Uncertainty in Artificial Intelligence, Windsor, Ont., 1989, pp. 351–360.

    Google Scholar 

  • R. R. Yager, “Applications and extensions of OWA aggregations.” Int. J. of Man-Machine Studies (to appear).

    Google Scholar 

  • M. O’Hagan, ‘Aggregating template rule antecedents in real-time expert systems with fuzzy set logic.” Int. J. of Man-Machine Studies, (to appear).

    Google Scholar 

  • J. Gordon and E. H. Shortliffe, “The Dempster–Shafer theory of evidence.” In: Rule-Based Expert Systems: the MYCIN Experiments of the Stanford Heuristic Programming Project, edited by B. G. Buchanan and E. H. Shortliffe, Addison Wesley, 1984, pp. 272–292.

    Google Scholar 

  • J. Gordon and E. H. Shortliffe, “A method for managing evidential reasoning in a hierarchical hypothesis space.” Artificial Intelligence, 26, 1985, pp. 323–357.

    Article  MathSciNet  Google Scholar 

  • J. D. Lowrance and T. D. Garvey, “Evidential reasoning: A developing concept.” In: IEEE Int. Conf. on Cybernetics and Society, Seattle, WA, 1982, pp. 6–9.

    Google Scholar 

  • J. D. Lowrance, T. D. Garvey and T. M. Strat, “A framework for evidential-reasoning systems.” Proceedings of the 5th National Conference on Artificial Intelligence (AAAI), Philadelphia, 1986, pp. 896–903.

    Google Scholar 

  • V. Quiggin, “A theory of anticipated utility.” J. of Economic Behavior and Organization, 3, 1982, pp. 323–343.

    Article  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Yager, R.R. (2008). Decision Making Under Dempster–Shafer Uncertainties. In: Yager, R.R., Liu, L. (eds) Classic Works of the Dempster-Shafer Theory of Belief Functions. Studies in Fuzziness and Soft Computing, vol 219. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44792-4_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-44792-4_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25381-5

  • Online ISBN: 978-3-540-44792-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics