Application of Non-convex Fuzzy Variables to Fuzzy Structural Analysis

  • Uwe Reuter
Part of the Advances in Soft Computing book series (AINSC, volume 48)


Data situation in engineering is usually characterized by uncertainty. Fuzzy set theory provides adequate modeling of specific uncertainty phenomena. In this paper a new approach for modeling and processing of imprecise data by means of non-convex fuzzy variables is presented. For numerical processing an enhanced discretization of non-convex fuzzy variables is introduced. Furthermore fuzzy structural analysis is enhanced in order to be applicable to non-convex fuzzy variables. Fuzzy structural analysis under consideration of non-convex fuzzy variables is demonstrated by way of a two bay steel structure.


Imprecise data Non-convex fuzzy variables Discretization Fuzzy structural analysis 


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  1. 1.
    Helton, J.C., Burmaster, D.E.: Special issue on the treatment of aleatory and epistemic uncertainty. Reliab. Eng. System Saf. 54(2–3), 91–262 (1996)CrossRefGoogle Scholar
  2. 2.
    Möller, B., Reuter, U.: Uncertainty Forecasting in Engineering. Springer, Heidelberg (2007)MATHGoogle Scholar
  3. 3.
    Möller, B., Graf, W., Beer, M.: Fuzzy structural analysis using α-level optimization. Comput. Mech. 26(6), 547–565 (2000)MATHCrossRefGoogle Scholar
  4. 4.
    Viertl, R.: Statistical Methods for Non-Precise Data. CRC Press, Boca Raton (1996)Google Scholar
  5. 5.
    Wood, K.L., Otto, K.N., Antonsson, E.K.: Engineering design calculations with fuzzy parameters. Fuzzy Sets Syst. 52, 1–20 (1992)CrossRefGoogle Scholar
  6. 6.
    Zadeh, L.A.: Fuzzy sets. Information & Control 8, 338–353 (1965)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Zimmermann, H.J.: Fuzzy Set Theory and Its Applications. Kluwer Academic Publishers, Boston (1992)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Uwe Reuter
    • 1
  1. 1.Department of Civil EngineeringTechnische Universität DresdenDresdenGermany

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