During the last decade, the application of fuzzy numbers in the civil engineering domain has evolved from small academic applications to large scale industrial cases. The most popular algorithm to perform the involved fuzzy calculations is the Transformation Method [
], although the application area of this method is limited by the requirement of monotonic input-output relationships on the one hand, and by the number of uncertain variables on the other hand: in case of non-monotonic input-output relationships, the Transformation Method may lead to an underestimation of the uncertainty on response variables, and the computational cost increases exponentially with the number of uncertain variables.
In the present paper, the Gradual α-level Decreasing (GαD) algorithm is presented as an alternative to the Transformation Method. This algorithm is based on the observation that the set of extrema with varying α-level is formed by continuous curves. In order to obtain the membership function of the output, the α-level is lowered step-by-step, whereby at each level, the extrema are searched in the vicinity of the extrema of the previous α-level.
The GαD-algorithm is applied to the analysis of the fuzzy frequency response function of a composite floor. A total of six uncertain variables is considered, including the material properties of the floor, the damping ratio and the boundary conditions. Comparison of the fuzzy FRF obtained with the Transformation Method and with the GαD algorithm (figure 1) shows that the resonance response uncertainty is underestimated by the Transformation Method, while it is evaluated correctly by the GαD-algorithm.
Fuzzy FRF of a composite floor