## 2 Model of NSOFCMNN
### Novel Self-Organizing Adjustment Mechanism  
This paper proposes a new self-organization adjustment mechanism that can automatically adjust the number of layers and blocks of the NSOFCMNN according to the size of the input data. For a traditional FCMNN, most of them set a fixed number of network layers \(n_{j}\) and blocks \(n_{k}\) to improve the generalization ability and learning accuracy of the fuzzy cerebellar model neural network. However, for different input data \(\mathbf{P}\), the fixed number of layers and blocks cannot obtain a better learning effect. When a neural network has a large amount of input data with a wide range of values, a small number of layers or blocks cannot approximate the ideal output well, and the number of layers and blocks of the network needs to be increased. However, when a small amount of data with a small value range is obtained, the large number of layers or blocks will slow down the operation speed of the neural network of the cerebellar model, and the learning efficiency is not ideal. At this time, it is necessary to consider reducing redundant blocks or redundant layers. Therefore, a novel self-organizing adjustment mechanism is established in this section. According to these rules, it is determined whether the number of layers and blocks need to be increased or decreased. If not, it means that the number of layers and blocks at this time are ideal values. (1) Increase the number of layers and blocks  
For constructing a self-organizing fuzzy cerebellum model neural network, it is first necessary to put in place a set of rules to judge and determine whether to add a new number of layers and blocks in the \"Association Memory\" space, and at the same time create a hypercube of new layers and blocks in the network part of the \"Weight Memory\" space and the part of the new layer and block corresponding to the \"Weight Memory\" space. The number of existing layers and blocks can be described as clusters. Depending on the input data, if the input data fall within the range of the cluster, it means that the input data belong to the current cluster, and there is no need to add new layers and blocks. There are layers and blocks and other rules to update. In the \"Associative Memory\" layer, the average distance \(\mathbf{AR}_{jk}\) is defined as:  
\[ \begin{array}{l}\mathbf{AR}_{jk}(\mathbf{P})=\left\|\mathbf{P}-\mathbf{\alpha}_{jk}\right\|_ {2}\\ forj=1,2,\cdots,n_{j},\ k=1,2,\cdots,n_{k}\end{array}  \tag{13}\]  
where \(\mathbf{\alpha}=\left[\alpha_{1 jk},\cdots,\alpha_{ijk}\right]^{T},i=1,\cdots,n_{i}\). Using the MAX-MIN method, the average distance \(\mathbf{AR}_{jk}\) of each layer and each block is traversed to determine whether to increase the number of layers. \[\mathbf{g}=\arg\min_{1\leq j\leq n_{j}}\ \min_{1\leq k\leq n_{k}}\mathbf{AR}_{jk}(\mathbf{P}) \tag{14}\]  
where \(\mathbf{g}=\left(\hat{j},\hat{k}\right)\), \(\hat{j}\) and \(\hat{k}\) represent the \(\hat{j}\)th layer and the \(\hat{k}\)th block to which the smallest block in these blocks belongs among all the blocks with the smallest average distance in each layer. By setting a minimum value \(T_{n}\), if \(\mathbf{AR}_{\mathbf{g}}(\mathbf{P})>T_{n}\) is satisfied, that is, in the blocks with the smallest average distance of each layer corresponding to all inputs, the average distance \(\mathbf{AR}_{jk}\) of the smallest blocks in these blocks, if in all input dimensions, is the largest \(\mathbf{AR}_{jk}\) If it is greater than or equal to \(T_{n}\), a new layer node and block node are generated at the same time. \[\max_{i}\mathbf{AR}_{jk}(\mathbf{P})\geq T_{n} \tag{15}\]  
This method means that if the distance between the input data and the center of the existing layer nodes in the cluster is greater than the set minimum value, the number of layers and blocks at the moment is too small, and a new one needs to be generated.