Dynamic Fuzzy Machine Learning

$(({\overset{\leftarrow}{r}}_{i e}, {\vec{r}}_{i e}) \land ({\overset{\leftarrow}{x}}_{i k}, {\vec{x}}_{i k}) \land ({\overset{\leftarrow}{r}}_{k j}, {\vec{r}}_{k j})) \leq (({\overset{\leftarrow}{r}}_{i e}, {\vec{r}}_{i e}) \land ({\overset{\leftarrow}{r}}_{k j}, {\vec{r}}_{k j})) \leq ({\overset{\leftarrow}{r}}_{i j}, {\vec{r}}_{i j}),$

and when $(({\overset{\leftarrow}{r}}_{i e}, {\vec{r}}_{i e}) \land ({\overset{\leftarrow}{r}}_{i e}, {\vec{r}}_{i e})) > ({\overset{\leftarrow}{r}}_{i j}, {\vec{r}}_{i j})$ is true, there is

$(({\overset{\leftarrow}{r}}_{i e}, {\vec{r}}_{i e}) \land ({\overset{\leftarrow}{x}}_{e k}, {\vec{x}}_{e k}) \land ({\overset{\leftarrow}{r}}_{k j}, \vec{r_{k j}})) \leq ({\overset{\leftarrow}{x}}_{e l}, {\vec{x}}_{e k}) \leq ({\overset{\leftarrow}{r}}_{i j}, {\vec{r}}_{i j}) .$

Hence, $({\overset{\leftarrow}{u}}_{i j}, {\vec{u}}_{i j}) \leq ({\overset{\leftarrow}{r}}_{i j}, {\vec{r}}_{i j}) (i \leq n, j \leq m);$ that is,

$(\overset{\leftarrow}{R}, \vec{R}) \circ (\overset{\leftarrow}{X}, \vec{X}) \circ (\overset{\leftarrow}{R}, \vec{R}) \subset (\overset{\leftarrow}{R}, \vec{R}) = (\overset{\leftarrow}{R}, \vec{R}) \circ (\overset{\leftarrow}{Q}, \vec{Q}) \circ (R$

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Dynamic Fuzzy Machine Learning by Fanzhang Li, Li Zhang, Zhao Zhang

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