Structural reliability analysis through fuzzy number approach, with application to stability

Structural reliability analysis in the presence of scarce or uncertain data is performed in the framework of possibility theory. Fuzzy numbers are used to define an equivalence class of probability distributions compatible with available data and corresponding upper and lower cumulative density functions. A procedure is then proposed to perform reliability analysis using extended fuzzy operations. It gives estimates of small and large fractiles of output variables which are conservative with respect to probability. A criterion to define the membership functions of fuzzy numbers starting from available information is also described. The method is used to perform reliability analysis against buckling. In civil engineering problems, usually very few data are available to define structural imperfections; often, normative requirements only are available in structural design stages. The results presented confirm the theoretical predictions described in Ref. [Comput. Meth. Appl. Mech. Eng. 160 (1998) 205], i.e., reliability analysis using fuzzy number theory gives conservative bounds of small/large fractiles with respect to probability.