LAUSR

Some traditional fuzzy reliability models quantify the system uncertainty based on possibility measure metric without self-duality, which leads to the undesired result that the sum of possibility of any one fuzzy set/event and its complementary set/event is not equal to one. To overcome this drawback, this paper formulates a new reliability metric tool based on self-dual credibility measure. Firstly, we introduce credilistic safety constraint to formulate credibilistic reliability optimization model on the basis of limit-state function. Then, several theorems are provided to show that the feasible domain generated by credibilistic safety constraint can be reformulated as the equivalent convex domain under mild assumptions, which enables credibilistic safety constraint to reformulate as the equivalent reliability constraint. Finally, one numerical example on the optimal design of three-bar truss structure is provided to show the applicability of the credibilistic reliability optimization model. By using out-of-sample back-testing, these comparison results are stated on the provided reliability level and the back-testing reliability level, which evidence the effectiveness of the optimal solution achieved by the proposed model for practical structural engineering.