# Qn: Qn scale measure of a trapezoidal fuzzy sample In FuzzyStatTra: Statistical Methods for Trapezoidal Fuzzy Numbers

## Description

This function calculates the scale measure Qn for a matrix of trapezoidal fuzzy numbers F. The employed metric in the calculation can be the 1-norm distance, the mid/spr distance or the (\varphi,θ)-wabl/ldev/rdev distance. The function first checks if the input matrix F is given in the correct form (tested by checkingTra).

## Usage

 1 Qn(F, type, a = 1, b = 1, theta = 1/3) 

## Arguments

 F matrix of dimension n x 4 containing n trapezoidal fuzzy numbers characterized by their four values inf0,inf1,sup1,sup0. The function implicitly checks if the matrix is in the correct form (tested by checkingTra). type number 1, 2 or 3: if type==1, the 1-norm distance will be considered in the calculation of the measure ADD. If type==2, the mid/spr distance will be considered. By contrast, if type==3, the (\varphi,θ)-wabl/ldev/rdev distance will be used. a number >0, by default a=1. It is the first parameter of a beta distribution which corresponds to a weighting measure on [0,1] in the mid/spr distance or in the (\varphi,θ)-wabl/ldev/rdev distance. b number >0, by default b=1. It is the second parameter of a beta distribution which corresponds to a weighting measure on [0,1] in the mid/spr distance or in the (\varphi,θ)-wabl/ldev/rdev distance. theta number >0, by default theta=1/3. It is the weight of the spread in the mid/spr distance and the weight of the ldev and rdev in the (\varphi,θ)-wabl/ldev/rdev distance.

See examples

## Value

The function returns the scale measure Qn, which is a real number.

## 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)

Asun Lubiano <lubiano@uniovi.es>, Sara de la Rosa de Saa <rosasara@uniovi.es>

checkingTra, Rho1Tra, DthetaphiTra, DwablphiTra
 1 2 3 4 5 6 7 # Example 1: F=SimulCASE1(10) Qn(F,3,1,1,1) # Example 2: F=matrix(c(1,3,2,2),nrow=1) Qn(F,2,5,1,1)