## 3 Study Methods and Evaluation Process
### Fuzzy C-Means Clustering Algorithm  
#### 3.3.1 Specific Principles  
In recent years, relying on the improvement of computer processing power, machine learning-related algorithms have been strongly developed in various disciplines, such as image recognition, language processing, engineering computing, document classification, and so on. Machine learning [23] is an important method for artificial intelligence research, and many scholars have researched new intelligent algorithms [24] or improved them based on existing algorithms with many results. Machine learning is broadly divided into supervised learning and unsupervised learning, and supervised learning requires a large number of samples for training to get the ideal model, and because the evaluation of underground space resources development is a complex evaluation system involving too many evaluation factors, the computational model is generally multidimensional or even a dozen dimensions, and because the geological conditions in different regions are often different, it is difficult to find training samples for supervised learning, so this paper chooses the unsupervised learning method. The unsupervised learning methods include deep learning [25], neural networks [26], Simulated annealing [27], and fuzzy algorithms [28]. According to the characteristics of the evaluation of subterranean space development involving qualitative and quantitative indicators--the data are fuzzy, and the evaluation results are hierarchical suitability classifications, fuzzy algorithms are most widely used in many fields such as pattern classification, image processing, and fuzzy rule processing, etc., compared to the applicable characteristics of other unsupervised learning methods, so this paper is more suitable for the calculation of fuzzy clustering algorithm analysis. The common fuzzy algorithms are the mean fuzzy algorithm and Gaussian fuzzy algorithm [29], among which the fuzzy C-mean clustering algorithm [30], as an improvement of the traditional fuzzy algorithm, takes the affiliation degree as any number in the interval [0 1], and the proposed basic basis is the criterion of \"minimizing the sum of squared intra-class weighted errors.\" The fuzzy C-mean is an improvement of the K-mean method. The objective function of the algorithm is the same as the K-mean, but the difference is that the fuzzy weight index is added to the objective function, which can be better applied in the underground space assessment work. The fuzzy C-mean clustering algorithm has been used in geotechnical engineering in many applications: slope stability analysis [31], arable land and agricultural land suitability evaluation, etc., but it has not been applied in the direction of underground space resource development evaluation, so the fuzzy C-mean clustering method is used to evaluate the underground space resource development as the innovation point of this paper. In this paper, the paradigm in the objective function of fuzzy C-mean clustering is used as weighted Euclidean distance to improve the commonly used Euclidean distance, and the value of each index is calculated by the hierarchical analysis method. That is, the weighted Euclidean distance is used to determine the distance or similarity between the sample and the clustering center. By finding the distance between the sample points and the best clustering center, the difference between the attribute values of the best clustering center points and the attribute values in the sample is minimized. The objective function is established as follows:  
\[J=\sum\limits_{i=1}^{C}\sum\limits_{j=1}^{n}u_{ij}^{m}\left\|x_{j}-c_{i} \right\|^{2} \tag{4}\]  
\(X_{j}\) is the sample point, ci is the \(i\)th clustering center, and m is the weighting index. Usually, m = 2, and \(U_{ij}\) is the fuzzy similarity matrix.