## 1 Introduction
Using concept lattice reduction theory to achieve reduction of stability evaluation index of surrounding rock can not only improve the effectiveness of evaluation index selection and accuracy of model, but also provide a reference for the prediction of surrounding rock stability in similar geological environment. Neural network model has great advantages in dealing with nonlinear classification evaluation and prediction of problems, and it is widely used [24; 25; 26]. Neural network classification method can solve the problem of strong subjective factors and experience alone in the past, which is conducive to increasing accuracy of reflecting the nonlinear relationship between the stability of roadway surrounding rock and evaluation index. Compared with the BP neural network, the probabilistic neural network (PNN) has the advantages of simple procedure, fast convergence, and no local optimal value [27; 28]. However, the probabilistic neural network model layer uses a Gaussian function as an activation function; that is, limited training data must be independent and identically distributed. In practice, the evaluation index of surrounding rock stability does not completely obey a Gaussian distribution. When the correlation between each index is uncertain, a probabilistic neural network is not necessarily satisfactory for a stability classification of the surrounding rock mass. The symmetric alpha-stable distribution has a broader mathematical expression than the Gaussian distribution, and its radial symmetry can also act as a radial basis function. Currently, improvement of the structure, kernel function and combination model enhances the applicability of neural network model [29; 30; 31]. Conceptual lattice reduction theory can be adapted to the uncertainties of correlation among the evaluation indexes. However, it possesses poor anti-noise ability. The improved probabilistic neural network model can have advantages in data training. Therefore, a combined model for predicting the surrounding rock stability in roadway based on conceptual lattice and symmetric alpha stable distribution probabilistic neural network is established. The model provides a new method for the stability evaluation of surrounding rock. In summary, this study involves the following novel aspects:1. To combat the uncertainty and concealment of the correlation between the prediction indexes of surrounding rock stability, a model based on grid multi-layer attribute reduction is established to reduce the attributes of the evaluation index, optimize the index, and improve model efficiency. 2. The synthetic minority over-sampling technique (SMOTE) is used to synthesize new training samples, so that the numbers of training samples are balanced. Introduction of symmetrical alpha stable distribution instead of Gaussian distribution as the basis function of the probabilistic neural network model gives the model a broader meaning of expression. 3. Concept lattice multi-level attribute reduction involves more efficient index optimization, however its promotion ability and anti-noise ability are poor. Since the probabilistic neural network has advantages in data training, a concept lattice and symmetrical alpha stable distribution probability neural network model for roadway surrounding rock stability prediction should be superior. The remainder of the paper is organized as follows. Section 2 shows the definition of concept lattice and the method of attribute reduction of concept lattice. Section 3 proposes a probabilistic neural network model based on symmetric Alpha-stable distribution and the optimization of the model's parameters by using genetic algorithm. Section 4 introduces the establishment of a Stable Prediction Model of Roadway Surrounding Rock Base on Concept Lattice Reduction and a Symmetric Alpha Stable Distribution Probability Neural Network. Section 5 represents the practical engineering application of the composite model. Section 6 summarizes the results of the analysis.