Research in Engineering Design

, Volume 1, Issue 3–4, pp 187–203 | Cite as

Representing imprecision in engineering design: Comparing fuzzy and probability calculus

  • Kristin L. Wood
  • Erik K. Antonsson
  • James L. Beck


A technique to perform design calculations on imprecise representations of parameters using the calculus of fuzzy sets has been previously developed [25]. An analogous approach to representing and manipulatinguncertainty in choosing among alternatives (design imprecision) using probability calculus is presented and compared with the fuzzy calculus technique. Examples using both approaches are presented, where the examples represent a progression from simple operations to more complex design equations. Results of the fuzzy sets and probability methods for the examples are shown graphically. We find that the fuzzy calculus is well suited to representing and manipulating the imprecision aspect of uncertainty in design, and that probability is best used to represent stochastic uncertainty.


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  1. 1.
    E.K. Antonsson. Development and Testing of Hypotheses in Engineering Design Research.ASME Journal of Mechanisms, Transmissions, and Automation in Design, 109:153–154, June 1987Google Scholar
  2. 2.
    T.J. Beltracchi and G.A. Gabriele. Observations on extrapolations using parameter sensitivity derivatives. In S.S. Rao, ed.,Advances in Design Automation-1988, Vol. DE-Vol. 14, pp. 15–173, New York, September 1988. ASMEGoogle Scholar
  3. 3.
    T.J. Beltracchi and G.A. Gabriele. A RQP based method for estimating parameter sensitivity derivatives. In S.S. Rao, ed.,Advances in Design Automation-1988, Vol. DE-Vol. 14, pp. 155–164, New York, September 1988. ASMEGoogle Scholar
  4. 4.
    D.I. Blockley. Fuzziness, probability, and fril. In4th Int. Conf. Struc. Safety Reliability, Kobe, Japan, May 1985Google Scholar
  5. 5.
    C.B. Brown. Analytical methods for environmental assessment and decision making.Regional Environmental Systems, pp. 181–206, June 1977Google Scholar
  6. 6.
    C.B. Brown and R.S. Leonard. Subjective uncertainty analysis. InASCE National Structural Engineering Meeting, Baltimore, Maryland, April 1971, Meeting Preprint 1388Google Scholar
  7. 7.
    J.J. Buckley. Decision making under risk: A comparison of Bayesian and fuzzy set methods.Risk Analysis, 3:157–168, 1983Google Scholar
  8. 8.
    D.M. Byrne and S. Taguchi. The Taguchi approach to parameter design. InQuality Congress Transaction—Anaheim, pp. 168–177. ASQC, May 1986Google Scholar
  9. 9.
    R.T. Cox.The Algebra of Probable Inference. Johns-Hopkins University Press, Baltimore, MD, 1961Google Scholar
  10. 10.
    J.R. Dixon. Iterative redesign and respecification: Research on computational models of design processes. In S.L. Newsome and W.R. Spillers, eds.,Design Theory '88, RPI, Troy, NY, June 1988. NSF. 1988 NSF Grantee Workshop on Design Theory and MethodologyGoogle Scholar
  11. 11.
    J.R. Dixon, M.R. Duffey, R.K. Irani, K.L. Meunier, and M.F. Orelup. A proposed taxonomy of mechanical design problems. In C.A. Tipnis and E.M. Patton, eds.,Computers in Engineering 1988, pp. 41–46, New York, June 1888. ASMEGoogle Scholar
  12. 12.
    W.M. Dong and F.S. Wong. Fuzzy weighted averages and implementation of the extension principle.Fuzzy Sets and Systems, 21(2):183–199, February 1987Google Scholar
  13. 13.
    Didier Dubois and Henri Prade.Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York, 1980Google Scholar
  14. 14.
    B.R. Gaines. Fuzzy and probability uncertainty logics.Information and Control, 38(2):154–169, August 1978Google Scholar
  15. 15.
    E.B. Haugen. Probabilistic Mechanical Design. John Wiley & Sons, New York, 1980Google Scholar
  16. 16.
    H. Jeffreys.Theory of Probability. Clarendon Press, third ed., 1961Google Scholar
  17. 17.
    A. Kaufmann and M.M. Gupta.Introduction to Fuzzy Arithmetic: Theory and Applications. Electrical/Computer Science and Engineering Series. Van Nostrand Reinhold Company, New York, 1985Google Scholar
  18. 18.
    W.J. Langner. Sensitivity analysis and optimization of mechanical system design. In S.S. Rao, ed.,Advances in Design Automation-1988, Vol. DE-Vol. 14, pp. 175–182, New York, September 1988. ASMEGoogle Scholar
  19. 19.
    R.E. Moore,Interval Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1966Google Scholar
  20. 20.
    G. Pahl and W. Beitz.Engineering Design. The Design Council, Springer-Verlag, New York, 1984Google Scholar
  21. 21.
    J.E. Shigley and L.D. Mitchell.Mechanical Engineering Design. McGraw-Hill Book Company, New York, 1983Google Scholar
  22. 22.
    J.N. Siddall.Probabilistic Engineering Design; Principles and Applications. Marcel Dekker, New York, 1983Google Scholar
  23. 23.
    G. Taguchi.Introduction to Quality Engineering. Asian Productivity Organization, Unipub, White Plains, NY, 1986Google Scholar
  24. 24.
    K.L. Wood and E.K. Antonsson. Computations with Imprecise Parameters in Engineering Design: Application and Example.ASME Journal of Mechnisms, Transmissions, and Automation in Design, June 1988. Submitted for reviewGoogle Scholar
  25. 25.
    K.L. Wood and E.K. Antonsson. Computations with Imprecise Parameters in Engineering Design: Background and Theory.ASME Journal of Mechanisms, Transmissions, and Automation in Design, 111(4) 616–625, December 1989Google Scholar
  26. 26.
    K.L. Wood, and E.K. Antonsson. Modeling Imprecision and Uncertainty in Preliminary Engineering Design.Mechanism and Machine Theory 25(3) 1990 (in press)Google Scholar
  27. 27.
    K.L. Wood, K.N. Otto, and E.K. Antonsson. A Formal Method for Representing Uncertainties in Engineering Design. In P. Fitzhorn, ed.,Proceedings of the First International Workshop on Formal Methods in Engineering Design, Fort Collins, Colorado, January 1990. Colorado State University. pp. 202–245Google Scholar
  28. 28.
    L.A. Zadeh. Fuzzy sets versus probability.Proc. IEEE, 68(3):421, 1980Google Scholar
  29. 29.
    L.A. Zadeh. Is probability theory sufficient for dealing with uncertainty in AI: a negative view. In L.N. Kanal and J.F. Lemmers, eds.,Uncertainty in Artificial Intelligence, pp. 103–116, Elsevier Science Publishers, 1986Google Scholar
  30. 30.
    L.A. Zadeh. Fuzzy sets.Information and Control, 8:338–353, 1965Google Scholar
  31. 31.
    L.A. Zadeh. Fuzzy logic and approximate reasoning.Synthese, 30:407–428, 1975Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • Kristin L. Wood
    • 1
  • Erik K. Antonsson
    • 2
  • James L. Beck
    • 2
  1. 1.Department of Mechanical EngineeringUniversity of TexasAustinUSA
  2. 2.Division of Engineering and Applied Science, 104–44California Institute of TechnologyPasadenaUSA

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