FuzzyStatTra (version 1.0)

Qn:

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 \((\varphi,\theta)\)-wabl/ldev/rdev distance. The function first checks if the input matrix F is given in the correct form (tested by checkingTra).

Usage

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 \((\varphi,\theta)\)-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 \((\varphi,\theta)\)-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 \((\varphi,\theta)\)-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 \((\varphi,\theta)\)-wabl/ldev/rdev distance.

Value

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

Details

See examples

See Also

checkingTra, Rho1Tra, DthetaphiTra, DwablphiTra

Examples

# 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)