# Fuzzy.variance: Calculates the variance by a chosen method: distance, exact... In FuzzySTs: Fuzzy Statistical Tools

## Description

Calculates the variance by a chosen method: distance, exact or approximation

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```Fuzzy.variance( data.fuzzified, method, dist.type = "DSGD", i = 1, j = 1, theta = 1/3, thetas = 1, p = 2, q = 0.5, breakpoints = 100, int.method = "int.simpson", plot = FALSE ) ```

## Arguments

 `data.fuzzified` a fuzzification matrix constructed by a call to the function FUZZ or the function GFUZZ, or a similar matrix. No NA are allowed. `method` choices are the following: "distance", "exact", "approximation1", "approxi- mation2", "approximation3", "approximation4", "approximation5". `dist.type` type of distance chosen from the family of distances. The different choices are given by: "Rho1", "Rho2", "Bertoluzza", "Rhop", "Delta.pq", "Mid/Spr", "wabl", "DSGD", "DSGD.G", "GSGD". `i` parameter of the density function of the Beta distribution, fixed by default to i = 1. `j` parameter of the density function of the Beta distribution, fixed by default to j = 1. `theta` a numerical value between 0 and 1, representing a weighting parameter. By default, theta is fixed to 1/3 referring to the Lebesgue space. This measure is used in the calculations of the following distances: d_Bertoluzza, d_mid/spr and d_phi-wabl/ldev/rdev. `thetas` a decimal value between 0 and 1, representing the weight given to the shape of the fuzzy number. By default, thetas is fixed to 1. This parameter is used in the calculations of the d_theta star and the d_GSGD distances. `p` a positive integer such that 1 ≤ p < infinity, referring to the parameter of the Rho_p and Delta_pq. By default, p is fixed to 2. `q` a decimal value between 0 and 1, referring to the parameter of the metric Delta_pq. By default, q is fixed to 0.5. `breakpoints` a positive arbitrary integer representing the number of breaks chosen to build the numerical alpha-cuts. It is fixed to 100 by default. `int.method` the integration method could be one of the following four methods: "int.0", "int.t", "int.ct" and "int.simpson". `plot` fixed by default to "FALSE". plot="TRUE" if a plot of the fuzzy number is required.

## Value

If the parameter method = "distance", returns a numerical value. If else, returns the numerical α-cuts of the estimated fuzzy variance.

## Examples

 ```1 2 3 4 5 6 7 8``` ```data <- matrix(c(1,2,3,2,2,1,1,3,1,2),ncol=1) MF111 <- TrapezoidalFuzzyNumber(0,1,1,2) MF112 <- TrapezoidalFuzzyNumber(1,2,2,3) MF113 <- TrapezoidalFuzzyNumber(2,3,3,3) PA11 <- c(1,2,3) data.fuzzified <- FUZZ(data,mi=1,si=1,PA=PA11) Fuzzy.variance(data.fuzzified, method = "approximation5", plot=TRUE) Fuzzy.variance(data.fuzzified, method = "distance") ```

FuzzySTs documentation built on July 8, 2020, 7:17 p.m.