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This paper discusses the damage identification in the mooring line system of a floating wind turbine (FWT) exposed to various environmental loads. The proposed method incorporates a non-probabilistic method into artificial neural networks (ANNs). The non-probabilistic method is used to overcome the problem of uncertainties. For this purpose, the interval analysis method is used to calculate the lower and upper bounds of ANNs input data. This data contains some of the natural frequencies utilized to train two different ANNs and predict the output data which is the interval bounds of mooring line stiffness. Additionally, in order to reduce computational time and more importantly, identify damage in various conditions, the proposed method is trained using constant loads (CL) case (deterministic loads, including constant wind speed and airy wave model) and is tested using random loads (RL) case (including Kaimal wind model and JONSWAP wave theory). The superiority of this method is assessed by applying the deterministic method for damage identification. The results demonstrate that the proposed non-probabilistic method identifies the location and severity of damage more accurately compared to a deterministic one. This superiority is getting more remarkable as the difference in uncertainty levels between training and testing data is increasing.