generator: Simulation of fuzzy random variables (FRV)

In SAFD: Statistical Analysis of Fuzzy Data

Description

The second procedure described in [1] is implemented. Given an input dataframe V in the correct format (tested by checking), which will be the expectation of the simulated FRV first decomposer(V) is called. Loosely speaking, the dataframe Y returned by decomposer, which contains the "coordinates" of V with respect to a certain "basis" (see [1]), is perturbated stochastically in order to generate a new polygonal fuzzy number. The distributions used for these perturbations can be selected in the call of the function, however, in this version only a few choices are possible: (1) The perturbation of the centre of the 1-cut pertV has to be of the form norm(0,sigma) or unif(-a,a), sigma,a>0. (2) The perturbation of the left part of the fuzzy set pertL has to be of the form chisq(1), exp(1) or lnorm(a,b) with expectation=1. (3) The perturbation of the right part of the fuzzy set pertR has to be of the same form as that for the left part.

Usage

generator(V, pertV = list(dist = "norm", par = c(0, 1)), 
             pertL = list(dist = "chisq", par = c(1)), 
             pertR = list(dist = "chisq", par = c(1)))

Arguments

V	...polygonal fuzzy set in the correct format (tested by checking)
pertV	...list containing elements "dist" and "par". "dist" denotes the chosen distribution family (normal or uniform) and "par" the corresponding parameters.
pertL	...list containing elements "dist" and "par". "dist" denotes the chosen distribution family (chisq or lnorm) and "par" the corresponding parameters.
pertR	...list containing elements "dist" and "par". "dist" denotes the chosen distribution family (chisq or lnorm) and "par" the corresponding parameters.

Details

See examples

Value

Given correct input data, the function returns a polygonal fuzzy number that can be seen as a realisation of a FRV with expectation V (see [1]).

Note

In case you find (almost surely existing) bugs or have recommendations for improving the functions comments are welcome to the above mentioned mail addresses.

Author(s)

Wolfgang Trutschnig <[e-mail]>, Asun Lubiano <[e-mail]>

References

[1] Gonzalez-Rodriguez, G., Colubi, A., Trutschnig, W.: Simulation of fuzzy random variables, Information Sciences, 179(5), pp. 642-653 (2009)

See Also

See Also as decomposer

Examples

#Example:
data(XX)
V<-translator(XX[[3]],100)
YY<-vector("list",length=100)
  for(i in 1:100){
   YY[[i]]<-generator(V,,,)
   }
M<-Mmean(YY) 
plot(M,type="l",xlim=c(-3,4))
lines(V,type="l",col="red",lwd=2)

Example output

SAFD documentation built on July 3, 2019, 5:02 p.m.