The authors give some remarks to the term risk regarding its use for the assessment of abandoned mine sites. These remarks are based on the recommendation Geotechnical Investigation and Evaluation of Abandoned Mine Sites developed by the working committee Abandoned Mining of the German Society for Geotechnical Engineering (DGGT) and the German Society for Mine Surveying (DMV), published in 2004.By this recommendation, the risk is defined as a product of the occurrence probability and the extent of damage of an unwanted event. The occurrence probability for each unwanted event is described by the linguistic terms in all probability, probable, less probable or practically impossible. The extent of damage for each unwanted event is described by the linguistic terms insignificant, small, high or very high. A matrix out of these terms is used to define schematically an explicit limiting risk for each unwanted event.The authors point out that a schematic determination of limiting risk should be supported by an unique and comprehensible evaluation of all significant risk factors and parameters influencing the extent of damage. Fuzzy sets can be used instead of a discreet classification leading to more plausible results. The processing of linguistic terms by a fuzzy logic system is demonstrated.