为了经济合理地治理金属矿采空区，建立了相对差异函数的采空区危险性识别模型。首先建立含14个指标的采空区危险性识别指标体系，并采用相对差异函数确定评价指标对评价级别的相对隶属度和熵权法、层次分析法（AHP）确定评价指标的组合权重；然后计算采空区危险性对评价级别的综合相对隶属度和级别特征值；最后根据级别特征值的平均值确定采空区的危险性级别。将该模型运用于某锡矿山8个采空区的危险性评价识别中，确定了各采空区的危险性级别，识别结果与未确知测度理论法识别结果相一致，符合现场实际。研究结果表明：该模型可通过自身参数的4种组合来提高采空区危险性识别结果的可靠性，为采空区危险性识别提供了一种新的方法。

Numerous of underground goaf left by metal mine mining not only bring a series of safety and environmental problems to the society，but also affect the development of mineral resources and the healthy and sustainable development of the national economy.The risk recognition of metal mine underground goaf is an important basis of its treatment，so accurately identify the danger of the goaf has become one of the problems to be solved urgently in the safety supervision of government departments and the safety production of mining enterprises.It has been difficult to accurately recognize metal mine underground goaf risk for many factors will influence the stability of underground goaf，and coexistence of quantitative and qualitative factors，and the existence of contradictions between these factors.In order to accurately identify the risk of metal mines underground goaf and manage the goaf economically and rationally，a risk recognition model of metal mine underground goaf based on relative difference function was established.First，a risk recognition index system of metal mine underground goaf containing 14 indexes was constructed according to the risk factors such as hydrogeological factors，goaf parameters，and other factors.Then the relative membership degree of the indexes to evaluation levels was calculated by relative difference function，and the combined weight of the indexes was determined by entropy weight method and analytical hierarchy process.Afterwards，the comprehensive relative membership degree and level characteristic value of metal mine underground goaf risk to different evaluation levels was calculated under four different combinations of distance parameter and optimization criteria parameter，and the level of metal mine underground goaf risk was then to be determined by the average level characteristic value.Furthermore，the whole process was applied to the risk recognition of eight underground goafs a tin mine and their calculated risk level was grade Ⅱ，grade Ⅱ，grade Ⅱ，grade Ⅰ，grade Ⅲ，grade Ⅰ，grade Ⅲ，grade Ⅰ，grade Ⅲ and grade Ⅰ，respectively.The calculation results fully consistent with the recognition results of uncertainty measurement and also well accordant with the practical situation，it also provides a helpful theoretical basis for the mine’s further treatment of underground goaf and safety production.The results show that the above established risk recognition model can self-verify the recognition results by changing its four combinations of its own parameters （distance parameter and optimization criteria parameter），which reflects the model’s overall control over the essential law of the unity and opposites of evaluation indexes.The model can improve the recognized reliability of underground goaf risk and its identification process is simple and efficient，which provides a new method for underground goaf risk recognition.