# S.PLFN: Simulate a random sample from Piecewise Linear Fuzzy Numbers In Sim.PLFN: Simulation of Piecewise Linear Fuzzy Numbers

## Description

This function is able to produce / simulate a random sample from Piecewise Linear Fuzzy Numbers (PLFNs).

## Usage

 ```1 2``` ```S.PLFN(n, knot.n, type = "PLFN", X.dist, X.dist.par, slX.dist, slX.dist.par, srX.dist, srX.dist.par ) ```

## Arguments

 `n` the size of random sample of PLSNs. `knot.n` the number of knots; see package `FuzzyNumbers` for more details. `type` The possible values of this argument is ` type = c("Tri", "Tra", "PLFN", "PLFI") `. In other words, this function returned one of following fuzzy numbers: (1) Triangular Fuzzy Number ( when ` type = "Tri" `), (2) Trapezoidal Fuzzy Number ( when ` type = "Tra" `), (3) Piecewise Linear Fuzzy Number ( when ` type = "PLFN" `), and (4) Piecewise Linear Fuzzy Interval ( when ` type = "PLFI" `). `X.dist` The distribution name of the random variable (for simulate the core of random fuzzy number) is determined by characteristic element `T.dist`. The names of distributions is similar to `stats` package. `X.dist.par` A vector of distribution parameters (for simulate the core of random fuzzy number) with considered ordering in `stats` package. `slX.dist` The distribution name of the random variable (for simulate the left spread value of random fuzzy number) is determined by characteristic element `T.dist`. The names of distributions is similar to `stats` package. `slX.dist.par` A vector of distribution parameters (for simulate the left spread value of random fuzzy number) with considered ordering in `stats` package. `srX.dist` The distribution name of the random variable (for simulate the right spread value of random fuzzy number) is determined by characteristic element `T.dist`. The names of distributions is similar to `stats` package. `srX.dist.par` A vector of distribution parameters (for simulate the right spread value of random fuzzy number) with considered ordering in `stats` package.

## Value

Considering the `type` argument, this function returned/simulate/create one of following fuzzy numbers: (1) Triangular Fuzzy Number, (2) Trapezoidal Fuzzy Number, (3) Piecewise Linear Fuzzy Number, and (4) Piecewise Linear Fuzzy Interval.

## References

Gagolewski, M., Caha, J. (2015) FuzzyNumbers Package: Tools to deal with fuzzy numbers in R. R package version 0.4-1, https://cran.r-project.org/web/packages=FuzzyNumbers

Gagolewski, M., Caha, J. (2015) A guide to the FuzzyNumbers package for R (FuzzyNumbers version 0.4-1) http://FuzzyNumbers.rexamine.com

DISTRIB FuzzyNumbers FuzzyNumbers.Ext.2 Calculator.LR.FNs

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```library(FuzzyNumbers) # Let x ~~ ( X~N(0,1) ; s_X^l~Exp(3) ; s_X^r~beta(1,3) ) n=3; knot.n=3 Sam <- S.PLFN( n=3, knot.n=4, type="Tra", X.dist="norm", X.dist.par=c(0,1), slX.dist="exp", slX.dist.par=3, srX.dist="beta", srX.dist.par=c(1,3) ) Sam Sam[,,"X3"] # For plotting random fuzzy sample: xlim = c( min(Sam), max(Sam) ) plot( cuts.to.PLFN(Sam[,,1]), type="b", col=1, xlim=xlim ) plot( cuts.to.PLFN(Sam[,,2]), type="b", col=2, add=TRUE ) plot( cuts.to.PLFN(Sam[,,3]), type="b", col=3, add=TRUE ) abline( h=round((knot.n+1):0/(knot.n+1),4), lty=3, col="gray70") ```

### Example output

```, , X1

L         U
1   -0.3773801 0.2012215
0.8 -0.3939854 0.2013899
0.6 -0.4105907 0.2015582
0.4 -0.4271960 0.2017266
0.2 -0.4438013 0.2018949
0   -0.4604066 0.2020633

, , X2

L          U
1   -2.647724 -0.3366846
0.8 -2.723382 -0.2966154
0.6 -2.799041 -0.2565462
0.4 -2.874699 -0.2164770
0.2 -2.950358 -0.1764078
0   -3.026016 -0.1363386

, , X3

L           U
1   -0.7625111 -0.15660038
0.8 -0.8375531 -0.11108919
0.6 -0.9125950 -0.06557800
0.4 -0.9876370 -0.02006681
0.2 -1.0626789  0.02544439
0   -1.1377209  0.07095558

L           U
1   -0.7625111 -0.15660038
0.8 -0.8375531 -0.11108919
0.6 -0.9125950 -0.06557800
0.4 -0.9876370 -0.02006681
0.2 -1.0626789  0.02544439
0   -1.1377209  0.07095558
```

Sim.PLFN documentation built on May 2, 2019, 5:51 a.m.