With the rapid development of modern society, the construction of hydropower stations has produced a series of ecological and environmental problems, which are becoming increasingly serious. The siting of hydropower stations is a multi-attribute decision-making problem. Considering the successful application of three-way decision (TWD) in multi attribute decision-making (MADM), combined with the advantages of intuitionistic fuzzy rough numbers (IFRNs) to deal with uncertainty problems, a new method of three-way MADM is proposed and applied this model to the siting of hydropower stations. The main contributions of this work are as follows: (1) According to characteristics of IFRNs, a method of calculating relative loss function based on IFRNs is proposed; (2) Combining advantages of objective weight and subjective weight calculation method, a new method for calculating combination attribute weight is put forward; (3) By extending the grey relational analysis method, a conditional probability calculation method based on IFRNs is proposed. (4) a three-way MADM method to classify and rank alternatives is proposed, and the corresponding algorithm description is given. Then, the calculation steps and ranking results of the method are illustrated by an example of hydropower station location. At last, we verified the feasibility and effectiveness of the method through comparative analysis, and analyzed the influence of each parameter on the classification and ranking results.