GLOB.EVAL {FuzzySTs}

Calculates the global evaluation of a linguistic questionnaire

Description

Calculates the global evaluation of a linguistic questionnaire

Usage

GLOB.EVAL(
  Full_Database,
  MI,
  bmi,
  SI,
  b_jkt,
  p_ind = rep(1/nrow(Full_Database), nrow(Full_Database)),
  distance.type,
  i = 1,
  j = 1,
  theta = 1/3,
  thetas = 1,
  p = 2,
  q = 0.5,
  breakpoints = 100
)

Arguments

Full_Database

the data set to evaluate.

MI

a numerical value representing the total number of main-items dividing the linguistic questionnaire.

bmi

an array referring to the initial weights of the main-items.

SI

an array representing the total numbers of sub-items per main-item.

b_jkt

a matrix of MI rows and max(SI) columns expressing the initial weights of each sub-item of a given main-item.

p_ind

a vector of the relative sampling weights of the units, for which length(p_ind) = nrow(data). If the weights are not relative, the following expression should be applied on the vector:

\frac{p_{ind}}{\sum_{i=1}^{n} p_{ind}}.

If no sampling weights are used, the vector of weights is reduced to a vector of values 1, i.e. rep(1, nrow(data)).

distance.type

type of distance chosen from the family of distances, set by default to the signed distance. 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 \le p < infinity, referring to the parameter of the Rho_p and Delta_pq.

q

a decimal value between 0 and 1, referring to the parameter of the metric Delta_pq.

breakpoints

a positive arbitrary integer representing the number of breaks chosen to build the numerical alpha-cuts. It is fixed to 100 by default.

Value

A data set of individual evaluations, for which the number of observations is exactly the same as the initial data set.

Examples

data <- matrix(c(3,4,2,3,3,2,4,3,3,4,3,4,4,2,5,3,4,4,3,3,3,4,4,3,
3,3,4,3,3,3,3,4,4,3,5,3,4,3,3,3), ncol = 4)
data <- as.data.frame(data)
MI <- 2
SI1 <- 2
SI2 <- 2
SI <- c(SI1,SI2)
b_j <- c(1/2,1/2)
b_jk <- matrix(c(0.5,0.5,0.5,0.5),nrow=2) 
PA11 <- c(1,2,3,4,5)
PA12 <- c(1,2,3,4,5)
PA21 <- c(1,2,3,4,5)
PA22 <- c(1,2,3,4,5)
# ------------------
MF111 <- TrapezoidalFuzzyNumber(0,2,2,7)
MF112 <- TrapezoidalFuzzyNumber(2,7,7,15)
MF113 <- TrapezoidalFuzzyNumber(7,15,15,23)
MF114 <- TrapezoidalFuzzyNumber(15,23,23,28)
MF115 <- TrapezoidalFuzzyNumber(23,28,28,30)
MF11 <- GFUZZ(data, 1, 1, PA11, spec="Identical", breakpoints = 100)
# ------------------
MF121 <- TrapezoidalFuzzyNumber(0,2,2,7)
MF122 <- TrapezoidalFuzzyNumber(2,7,7,15)
MF123 <- TrapezoidalFuzzyNumber(7,15,15,23)
MF124 <- TrapezoidalFuzzyNumber(15,23,23,28)
MF125 <- TrapezoidalFuzzyNumber(23,28,28,30)
MF12 <- GFUZZ(data, 1, 2, PA12, spec="Identical", breakpoints = 100)
# ------------------
MF211 <- TrapezoidalFuzzyNumber(0,2,2,7)
MF212 <- TrapezoidalFuzzyNumber(2,7,7,15)
MF213 <- TrapezoidalFuzzyNumber(7,15,15,23)
MF214 <- TrapezoidalFuzzyNumber(15,23,23,28)
MF215 <- TrapezoidalFuzzyNumber(23,28,28,30)
MF21 <- GFUZZ(data, 2, 1, PA21, spec="Identical", breakpoints = 100)
# ------------------
MF221 <- TrapezoidalFuzzyNumber(0,2,2,7)
MF222 <- TrapezoidalFuzzyNumber(2,7,7,15)
MF223 <- TrapezoidalFuzzyNumber(7,15,15,23)
MF224 <- TrapezoidalFuzzyNumber(15,23,23,28)
MF225 <- TrapezoidalFuzzyNumber(23,28,28,30)
MF22 <- GFUZZ(data, 2, 2, PA22, spec="Identical", breakpoints = 100)
# ------------------
range <- matrix(c(0,0,0,0,28,28,28,28), ncol=2)
ind.eval <- IND.EVAL(data,MI,b_j,SI,b_jk, range = range, distance.type ="DSGD.G")
GLOB <- GLOB.EVAL(data, MI, b_j, SI, b_jk, distance.type ="GSGD")