frbs (version 3.2-0)

# GFS.LT.RS: GFS.LT.RS model building

## Description

This is the internal function that implements genetic lateral tuning and rule selection of linguistic fuzzy systems (GFS.LT.RS). It is used to solve regression tasks. Users do not need to call it directly, but just use frbs.learn and predict.

## Usage

GFS.LT.RS(data.train, popu.size = 10, range.data, num.labels,
persen_mutant, max.gen = 10, mode.tuning = "GLOBAL",
type.tnorm = "MIN", type.snorm = "MAX",
type.implication.func = "ZADEH", type.defuz = "WAM",
rule.selection = FALSE, range.data.ori)

## Arguments

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.

popu.size

the size of the population which is generated in each generation.

range.data

a matrix representing interval of data.

num.labels

a matrix representing the number of linguistic terms in each variables.

persen_mutant

a real number between 0 and 1 determining the probability of mutation.

max.gen

the maximal number of generations of the genetic algorithm.

mode.tuning

a type of tuning which are "LOCAL" or "GLOBAL".

type.tnorm

a type of t-norm. See inference.

type.snorm

a type of s-norm. See inference.

type.implication.func

a type of implication function. See WM.

type.defuz

a type of defuzzification methods. See defuzzifier.

rule.selection

a boolean value representing whether performs rule selection or not.

range.data.ori

a matrix containing the ranges of the original data.

## Details

This method was proposed by R. Alcala et al. GFS.LT.RS implements a evolutionary algorithm for postprocessing in constructing FRBS model. It uses a new rule representation model based on the linguistic 2-tupples representation that allows the lateral displacement of the labels. This function allows two different tuning which are global and local tuning.

Regarding with evolutionary algorithms, the following are main components:

• coding scheme and initial gene pool;

• chromosome evalution;

• crossover operator;

• restarting approach;

• evolutionary model;

In first time, population is constructed by Wang & Mendel's technique. Mean square error (MSE) is used to calculate chromosome evaluation. This method performs BLX-a in crossover process. Additionally, rule selection method is performed in order to minimize the number of rules.

## References

R. Alcala, J. Alcala-Fdez, and F. Herrera, "A proposal for the genetic lateral tuning of linguistic fuzzy systems and its interaction with rule selection", IEEE Trans. on Fuzzy Systems, Vol. 15, No. 4, pp. 616 - 635 (2007).