This is the internal function that implements the fuzzy rule-based classification
system with weight factor (FRBCS.W). It is used to solve classification tasks.
Users do not need to call it directly,
but just use `frbs.learn`

and `predict`

. This method is
suitable only for classification problems.

```
FRBCS.W(range.data, data.train, num.labels, num.class, type.mf,
type.tnorm = "MIN", type.snorm = "MAX",
type.implication.func = "ZADEH")
```

range.data

a matrix (\(2 \times n\)) containing the range of the normalized data, where \(n\) is the number of variables, and first and second rows are the minimum and maximum values, respectively.

data.train

a matrix (\(m \times n\)) of normalized data for the training process, where \(m\) is the number of instances and \(n\) is the number of variables; the last column is the output variable. Note the data must be normalized between 0 and 1.

num.labels

a matrix (\(1 \times n\)), whose elements represent the number of labels (linguistic terms); \(n\) is the number of variables.

num.class

an integer number representing the number of labels (linguistic terms).

type.mf

the type of the shape of the membership functions.

type.tnorm

the type of t-norm. See `inference`

.

type.snorm

the type of s-norm. See `inference`

.

type.implication.func

the type of implication function. See `WM`

.

This method is adopted from Ishibuchi and Nakashima's paper. Each fuzzy IF-THEN rule consists of antecedent linguistic values and a single consequent class with certainty grades (weights). The antecedent part is determined by a grid-type fuzzy partition from the training data. The consequent class is defined as the dominant class in the fuzzy subspace corresponding to the antecedent part of each fuzzy IF-THEN rule and the certainty grade is calculated from the ratio among the consequent class. A class of the new instance is determined by the consequent class of the rule with the maximal product of the compatibility grade and the certainty grade.

H. Ishibuchi and T. Nakashima, "Effect of rule weights in fuzzy rule-based classification systems", IEEE Transactions on Fuzzy Systems, vol. 1, pp. 59 - 64 (2001).

`FRBCS.eng`

, `frbs.learn`

, and `predict`