针对采空区稳定性评价具有模糊性、随机性以及评价指标等级呈有限区间正态分布等问题，考虑评价指标值突变对评价指标权重的影响，提出了基于变权联系云的采空区稳定性二维评价模型。首先选取12个评价指标构建采空区评价指标体系，并通过各指标联系云图反映其实际分布情况；然后利用博弈论和变权理论得到变权权重；最后计算采空区各评价指标对应等级的确定度和采空区的综合确定度，并根据最大隶属度原则确定采空区稳定性等级。为解决指标等级归属不一致的问题，引入模糊熵作为第二维评价系统，以表征采空区稳定性的复杂度。结果表明：变权联系云模型评价结果与实例应用结果一致，验证了该模型的可行性与合理性。

The instability of the goaf poses serious threat to mine safety，and its stability is affected by many uncertain factors.Therefore，it is very important to evaluate the stability of the goaf.Many factors affect the result in the evaluation process，for instance，many ambiguity and randomness information exist in the evaluation of the goaf stability，the evaluation index interval normally distributed，dynamic combination of different evaluation index affect the weight values，and the inconsistency of the indicator level.In order to solve these problems，a two-dimensional evaluation model of goaf stability based on variable-weighted cloud was established.On the basis of comprehensive consider the actual situation of the goaf and related research results，the stability evaluation system and grading standards of the goaf were established.The digital characteristics of the contact cloud of each evaluation index belonging to different levels were calculated respectively，and then the contact cloud maps were generated by using the contact cloud generator and Rstudio software.Substituting the measured values of the sample indicators into the contact cloud model to calculate the degree of certainty of the contact cloud.After that，the subjective weight and objective weight were calculated by using the analytic hierarchy process and the entropy weight method respectively.Considering the advantages and disadvantages of the subjective and objective weighting methods，the game theory was used to fuse these two empowerment methods to obtain the optimized comprehensive weight.Considering that comprehensive weights calculated by game theory were constant weight，which could not reflect the influence of the index value on the weight，the variable weight theory was used to change the weight to obtain the variable weight，so as to better display the effect of dynamic change of the index value on evaluation result.The comprehensive determination degree of the goaf was then obtained by calculating the certainty degree of measured index value belongs to each contact level cloud and the final variable weight.After that，the stability level of the gob was determined according to the principle of maximum membership degree.In order to solve the problem of inconsistent index level attribution，fuzzy entropy was introduced as the second dimension evaluation auxiliary parameter to characterize the stability complexity of the goaf.The model was applied to engineering practice and compared with traditional cloud model and matter-element extension model，the evaluation results are basically the same.The results show that the stability evaluation model of the goaf is scientific and reasonable，and it provides a new idea for the stability evaluation of goaf and the stability evaluation of similar projects.