Dynamic Fuzzy Machine Learning

Definition 6.10 Let $\left({\overleftarrow{r}}_{ij}^t,{\overleftarrow{r}}_{ij}^t\right)=\left(\left({\overleftarrow{l}}_{ij}^t,{\overrightarrow{l}}_{ij}^t\right),\left({\overleftarrow{m}}_{ij}^t,{\overrightarrow{m}}_{ij}^t\right),\left({\overleftarrow{n}}_{ij}^t,{\overrightarrow{n}}_{ij}^t\right)\right)$ be the DFD given by the t th expert, where i, j = 1, 2, . . ., nk, t = 1, 2, . . .N. Then, the relationship matrix of all the elements in the k th level with respect to the h th element in the (k − 1)th level is given by the following formula:

$M_{ij}^k=\frac{1}{N}\otimes \left(\left({\overleftarrow{r}}_{ij}^1,{\overrightarrow{r}}_{ij}^1\right)+\left({\overleftarrow{r}}_{ij}^2,{\overrightarrow{r}}_{ij}^2\right)+\cdots +\left({\overleftarrow{r}}_{ij}^N,{\overrightarrow{r}}_{ij}^N\right)\right).\left(6.13\right)$

The corresponding dynamic fuzzy comprehensive rate is

$S_i^k={\displaystyle \sum _{j=1}^{n_k}{M}_{ij}^k\otimes \frac{1}{{\displaystyle \sum _{i=1}^{N_k}{\displaystyle \sum _{j=1}^{n_k}{M}_{ij}^k}}}.}$