Fuzzy Sets pp 391-404 | Cite as

Fuzzy Concepts in the Analysis of Public Health Risks

  • Thomas B. Feagans
  • William F. Biller


Several important concepts encountered in public health risk analysis are not sharp in one sense or another. These concepts are discussed and a view is presented of how they should be treated in a regulatory context. The concepts of an adverse health effect, a highly qualified probability assessor, and an acceptable degree of risk are inherently imprecise. The concept of probability suitable for the purposes of regulatory risk assessment is precisely defined but in general does not result in sharp probability inputs to the probabilistic models required to generate risk estimates; rather, in general the probability inputs are upper and lower probabilities. Furthermore, in general there is secondary uncertainty about what (upper and lower) probabilities should represent the primary uncertainties that give rise to the risk being assessed. Hence, probability assignments need to be elicited from several probability assessors. These two divergences from unique probability assignments are propagated through the probabilistic model to the risk estimates. Hence, risk is a fuzzy concept in the sense that there does not generally exist a unique risk that an adverse event will occur in a given period of time, but rather distributions of upper and lower risk estimates.


Adverse Health Effect Probability Assignment Public Health Risk Fuzzy Concept Probability Judgment 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Black, “Margins of Precision,” Cornell University Press, Ithaca, New York (1970).Google Scholar
  2. 2.
    L. A. Zadeh, Fuzzy Sets, Inform, and Control, 8, 338–353 (1965).CrossRefGoogle Scholar
  3. 3.
    R. E. Bellman and L. A. Zadeh, Decision-Making in a Fuzzy Environment, Management Science, 17, 141–164 (1970).CrossRefGoogle Scholar
  4. 4.
    L. A. Zadeh, K. Fu, K. Tanaka, and M. Simura, eds., “Fuzzy Sets and their Applications to Cognitive and Decision Processes,” Academic Press, Inc., New York (1975).Google Scholar
  5. 5.
    M. M. Gupta, G. N. Saridis, and B. R. Gaines, eds., “Fuzzy Automata and Decision Processes,” North-Holland Publishing Co., New York (1977).Google Scholar
  6. 6.
    T. B. Feagans and W. F. Biller, “A Method for Assessing the Health Risks Associated with Alternative Air Quality Standards,” U.S. EPA, Office of Air Quality Planning and Standards (in preparation).Google Scholar
  7. 7.
    S. Leung, E. Goldstein, and N. Dalkey, “Human Health Damages from Mobile Source Air Pollution: A Delphi Study,” Vols. 1 and 2, performed for California Air Resources Board (April 1977).Google Scholar
  8. 8.
    R. A. Howard, J. E. Matheson, and D. W. North, “Decision Analysis for Environmental Protection Decisions,” prepared for National Academy of Sciences, SRI Project 5094, Menlo Park, CA (June 1977).Google Scholar
  9. 9.
    H. E. Kyburg, Jr. and H. E. Smokier, eds., “Studies in Subjective Probability,” John Wiley and Sons, Inc., New York (1964).Google Scholar
  10. 10.
    C. S. Spetzler and C. A. S. Stael, von Holstein, Probability Encoding in Decision Analysis, Management Science, Vol. 22, No. 3 (November 1975).Google Scholar
  11. 11.
    B. O. Koopman, The Axioms and Algebra of Intuitive Probability, Annals of Mathematics, vol. 41, 269–292 (1940).CrossRefGoogle Scholar
  12. 12.
    B. O. Koopman, The Bases of Probability, Bulletin of the American Mathematical Society, vol. 46, 763–774 (1940).CrossRefGoogle Scholar
  13. 13.
    I. J. Good, “Probability and the Weighing of Evidence,” Hafner, New York (1950).Google Scholar
  14. 14.
    C. A. B. Smith, Consistency in Statistical Inference and Decision, J. of the Royal Statistical Society (Series B), vol. 23, 1–37 (1961).Google Scholar
  15. 15.
    A. P. Dempster, Upper and Lower Probabilities Induced by a Multi-valued Mapping, Annals of Mathematical Statistics, vol. 38, 325–339 (1967).CrossRefGoogle Scholar
  16. 16.
    R. J. Beran, On Distribution-Free Statistical Inference with Upper and Lower Probabilities, Annals of Math. Statistics, vol. 42, No. 1, pp. 157–168 (1971).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • Thomas B. Feagans
    • 1
  • William F. Biller
    • 2
  1. 1.Office of Air Quality Planning and StandardsU.S. Environmental Protection AgencyRTPUSA
  2. 2.East BrunswickUSA

Personalised recommendations