GFS: GFS model building

Description

This is the internal function that implements the genetic fuzzy systems (GFS) model. Users do not need to call it directly, but just use frbs.learn and predict

Usage

GFS(data.train, range.data, num.labels, popu.size,
    persen_cross, persen_mutant, max.iter,
    classification = FALSE, range.data.ori)

Arguments

data.train

a matrix(m x n) of 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.

range.data

a matrix(2 x 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 value, respectively.

num.labels

a matrix(1 x n), whose elements represent the number of labels (fuzzy terms); n is the number of variables.

popu.size

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

persen_cross

a real number between 0 and 1 representing the probability of crossover.

persen_mutant

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

max.iter

the maximal number of iterations.

classification

a boolean representing whether it is a classification problem or not.

range.data.ori

a matrix(2 x n) containing the range of the original data, where n is the number of variables, and first and second rows are the minimum and maximum value, respectively.

Details

This function is adopted from Jindrich Liska and Stephen S. Melsheimer's paper. GFS implements a genetic algorithm in order to determine the structure of the fuzzy IF-THEN rules and the membership function parameters. Genetic algorithms (GA) are a stochastic optimization technique that mimics natural selection. We conduct selection, uniform crossover, mutation, and the creep operator for the GA. One important thing when using a GA is to choose the representation of the solutions within the individuals. We split every individual to become two matrices which are a matrix of membership function parameters for all variables and a matrix of the structure of the fuzzy IF-THEN rules. Initially, one individual is generated using the techniques of Wang and Mendel, and the rest is generated at random. So, this method is always better or at least the same as the Wang and Mendel method. The fitness function is computed as the root mean square error for each individual.

References

Davis L., "Adaptive operator probabilities in genetic algorithm," ICGA'89 (1989).

Holland J. H., "Adaptation in natural and artificial systems," University of Michigan Press, Ann Arbor (1975).

Jindrich Liska and Stephen S. Melsheimer, "Complete design of fuzzy logic systems using genetic algorithm," Fuzzy Systems, IEEE World Congress on Computational Intelligence (1994).

Jindrich Liska and Stephen S. Melsheimer, "Design of fuzzy logic systems for nonlinear model identification," American Control Conference (1994).