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Plenty of mathematics researches provide feasibility to calculate the weights of geothermal controlling factors and have been applied in geothermal potential assessment. In order to avoid the disadvantages of subjective and objective weighting calculation methods, an extension theory integrated weighting method was put forward, by combining with the process of AHP and mean variance method. The improved method can reach an agreement on subjective understanding of impact factors’ roles and data-based calculation weights. Then by replacing the point values with intervals, the extension theory was used in classification of geothermal assessment, according to extension judgment matrix. The evaluation results showed perfect performance in classification of impact factors, especially in Wudalianchi area, where 10 out of 11 selected impact factors agreed well with the actual evaluation grades. The study can provide a guidance for primary stage of geothermal investigation including the impact factor selection, weights calculation for impact factors, and the factors’ classification in geothermal assessment.