Fuzzy fault tree analyses were used to investigate accident scenarios that involve radiological exposure to operators working in industrial γ-ray irradiation facilities. The HEART method, a first generation human reliability analysis method, was used to evaluate the probability of adverse human error in these analyses. This technique was modified on the basis of fuzzy set theory to more directly take into account the uncertainties in the error-promoting factors on which the methodology is based. Moreover, with regard to some identified accident scenarios, fuzzy radiological exposure risk, expressed in terms of potential annual death, was evaluated. The calculated fuzzy risks for the examined plant were determined to be well below the reference risk suggested by International Commission on Radiological Protection.