## 2 Model of NSOFCMNN
### Novel Self-Organizing Adjustment Mechanism
The new number of layers and blocks are given by:  
\[n_{j}(t+1)=n_{j}(t)+1 \tag{16}\]  
\[n_{k}(t+1)=n_{k}(t)+1 \tag{17}\]  
where \(n_{j}(t)\) is the number of existing layers and \(n_{k}(t)\) is the number of existing blocks. After new layers and blocks are generated, not only the layers and blocks of the \"Associative Memory\" space will be added, but also the layers and blocks of the receptive field will also increase. The center value and variance value of the Gaussian function will add new layer nodes and block nodes. The values of the new layer and block corresponding to the two parameters are set as:  
\[\alpha_{in_{j}n_{k}}=p_{i} \tag{18}\]  
\[\beta_{ijk}=\beta_{in_{j}n_{k}} \tag{19}\]  
(2) Reduce the number of layers  
The main purpose of reducing the layers is to improve the operation speed of the NSOFCMNN, and also use the MAX-MIN method to delete the redundant layers. Consider the \(j\)th layer value of the \(o\)th output:  
\[O_{oj}=\sum_{k=1}^{n_{k}}\omega_{jko}\psi_{jk},o=1,\cdots,n_{o},j=1,2,\cdots, n_{j} \tag{20}\]In formula (5), \(O_{o}\) is the output of the \(o\)th dimension. In formula (20), \(O_{oj}\) is the multiplication and summation of the \"Receptive-field\" space and \"Weight Memory\" space of the \(j\)th layer of the \(o\)th dimension. Next, the contribution ratio value \(RR_{oj}\) is defined as:  
\[ \begin{array}{c}RR_{oj}(P)=\frac{O_{oj}(P)}{O_{oj}(P)}\\ for\ o=1,\cdots,n_{o},\ j=1,2,\cdots,n_{j}\end{array}  \tag{21}\]  
\(RR_{oj}(P)\) represents the proportion of the output in the entire \(o\) dimension after the input data is transformed into the \"Receptive-field\" space of the fuzzy cerebellar model neural network and multiplied by the weight of the \"Weight Memory\" space of the \(j\)th layer. Therefore, the largest contribution layer of all output dimensions is found, and the layer \(\hat{\phi}\) with the smallest contribution is:  
\[\hat{\phi}=\arg\min_{1\leq j\leq n_{j}}\ \max_{1\leq o\leq n_{o}}RR_{oj}(P) \tag{22}\]  
By setting a minimum contribution value \(T_{m}\) of the layer, if \(RR_{oj}\leq T_{m}\) is satisfied, which means that for the \(o\)th dimension output, the contribution of a certain layer to the output is less than a set minimum contribution value, then the \(\hat{\phi}\)th layer at this moment is considered redundant and it should be deleted. At the same time, the corresponding layers of \"Associative Memory\" space, \"Weight Memory\" space and the center value and variance value of the Gaussian function will be reduced, and then the parameters will be updated according to the update formula. At this time, the new number of layers is given by:  
\[n_{j}(t+1)=n_{j}(t)-1 \tag{23}\]  
(3) Reduce the number of blocks  
The rules for reducing blocks have similar logic to the rules for reducing layers. Using the MAX-MIN method, the value h of the \(o\)th output at the \(k\)th block in the \(j\)th layer is considered as follows:  
\[O_{ojk}=\omega_{jko}\psi_{jk},o=1,\cdots,n_{o},j=1,2,\cdots,n_{j} \tag{24}\]  
The contribution ratio value \(KK_{ojk}\) is defined as:  
\[ \begin{array}{c}KK_{ojk}(P)=\frac{O_{ojk}(P)}{O_{oj}(P)}\\ for\ o=1,\cdots,n_{o},\ j=1,2,\cdots,n_{j}\\ and\ k=1,2,\cdots,n_{k}\end{array}  \tag{25}\]  
\(KK_{ojk}(P)\) represents the ratio of the input data after passing through the \"Receptive-field\" space of NSOFCMNN and the corresponding weight of the \"Weight Memory\" space of the \(k\)th block multiplied in the \(j\)th layer of the entire \(o\)th dimension. Then, the block with the largest proportion in the output of the \(j\)th layer of the \(o\)th dimension is found.