Learning

• Supervised learning: It induces an input-output mapping from a data set, called learning data set. It is usually limited to a MISO (multiple input single output) system. The learning data set includes $n$ items.

  
  

• Coverage index: Some items may activate the rules with a low matching degree. An item will be considered as inactive if its maximum matching degree over all rules is lower than a user chosen threshold (default value= 0.1. Inactive items are not managed by the FIS. The number of inactive items is used to define a coverage index, calculated as follows: $$CI = frac{A}{n}$$. A is the number of active items and n the number of rows in the data file.

  
  

• Performance indices, calculated from the active examples only.

  For a classification case:

  $$PI= \sum_{i = 1}^A mc(i)$$
  where $mc(i)$ equa;s 1 for a misclassified item, 0 otherwise.

  For a regression case, three indices are available:

  • $$PI = \frac{1}{A} \sqrt{\sum_{i = 1}^A\left\Vert \widehat{y_i} - y_i \right\Vert^2}$$
  • $$RMSE = \sqrt{\frac{1}{A} \sum_{i = 1}^A\left\Vert \widehat{y_i} - y_i \right\Vert^2}$$
  • $$MAE = \frac{1}{A}\sum_{i=1}^A \vert\widehat{y_i}-y_i\vert$$

  $PI$ is the historical accuracy index used by previous versions of FisPro, RMSE is the Root Mean Squared Error, et MAE is the Mean Absolute Error.