In this paper modeling of epistemic uncertainty in reliability analysis of structures under degradation of resistance has been brought into focus. Proposing a new method, random variables has been modeled in the form of fuzzy triangular numbers and applying alpha level set optimization method based on genetic algorithm and FORM method, the fuzzy time dependent reliability index of a steel corroded beam has been determined. The proposed method is operative in the problems in which most of random variables are fuzzy sets and in nonlinear limit state functions. The fuzzy time dependent reliability index including bounds of uncertainty, offers a more comprehensive evaluation of reliability of structures compared to classic methods of time dependent reliability analysis. Survey results showed the accuracy and efficiently of the proposed method in comparison to the alternative search approaches thorough lower computational effort.
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