# RI.hybridFS.FRST: Hybrid fuzzy-rough rule and induction and feature selection In RoughSets: Data Analysis Using Rough Set and Fuzzy Rough Set Theories

## Description

It is a function for generating rules based on hybrid fuzzy-rough rule induction and feature selection. It allows for classification and regression tasks.

## Usage

 `1` ```RI.hybridFS.FRST(decision.table, control = list()) ```

## Arguments

 `decision.table` a `"DecisionTable"` class representing the decision table. See `SF.asDecisionTable`. `control` a list of other parameters which consist of `type.aggregation` a list representing the type of aggregation. The default value is `type.aggregation = c("t.tnorm", "lukasiewicz")`. See `BC.IND.relation.FRST`. `type.relation` the type of indiscernibility relation. The default value is `type.relation = c("tolerance", "eq.3")`. See `BC.IND.relation.FRST`. `t.implicator` the type of implication function. The default value is `"lukasiewicz"`. See BC.LU.approximation.FRST.

## Details

It was proposed by (Jensen et al, 2009) attempting to combine rule induction and feature selection at the same time. Basically this algorithm inserts some steps to generate rules into the fuzzy QuickReduct algorithm (see `FS.quickreduct.FRST`. Furthermore, by introducing the degree of coverage, this algorithm selects proper rules.

This function allows not only for classification but also for regression problems. After obtaining the rules, predicting can be done by calling `predict` or `predict.RuleSetFRST`. Additionally, to get better representation we can execute `summary`.

## Value

A class `"RuleSetFRST"` which has similar components as `RI.GFRS.FRST` but in this case the `threshold` component is not included.

Lala Septem Riza

## References

R. Jensen, C. Cornelis, and Q. Shen, "Hybrid Fuzzy-rough Rule Induction and Feature Selection", in: IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), p. 1151 - 1156 (2009).

`RI.indiscernibilityBasedRules.RST`, `predict.RuleSetFRST`, and `RI.GFRS.FRST`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```########################################################### ## Example 1: Regression problem ########################################################### data(RoughSetData) decision.table <- RoughSetData\$housing7.dt control <- list(type.aggregation = c("t.tnorm", "lukasiewicz"), type.relation = c("tolerance", "eq.3"), t.implicator = "lukasiewicz") res.1 <- RI.hybridFS.FRST(decision.table, control) ########################################################### ## Example 2: Classification problem ############################################################## data(RoughSetData) decision.table <- RoughSetData\$pima7.dt control <- list(type.aggregation = c("t.tnorm", "lukasiewicz"), type.relation = c("tolerance", "eq.3"), t.implicator = "lukasiewicz") res.2 <- RI.hybridFS.FRST(decision.table, control) ```