IND.EVAL {FuzzySTs}

Calculates the individual evaluations of a linguistic questionnaire

Description

Calculates the individual evaluations of a linguistic questionnaire

Usage

IND.EVAL(
  Full_Database,
  MI,
  bmi,
  SI,
  b_jkt,
  range,
  distance.type,
  i = 1,
  j = 1,
  theta = 1/3,
  thetas = 1,
  p = 2,
  q = 0.5,
  breakpoints = 100,
  spec = "Identical"
)

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.

range

a vector of 2 elements giving the range of definition of the produced individual evaluations. The range is usually chosen in the interval between 0 and the maximum of the support set of all the membership functions modelling the data set.

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.

spec

specification of the fuzzification matrix. The possible values are "Identical" and "Not Identical".

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")