bertoluzza {SAFD}

Bertoluzza distance

Description

Given two polygonal fuzzy numbers X, Y in the correct format (testing by checking) the function calculates the Bertoluzza distance of X, Y. The parameter theta (being the weight of the spread) has to fulfill theta>0, by default theta=1/3 (which corresponds to the Lebesgue measure as weighting measure on [0,1]). For detailed explanation see the papers [1] and [2] below.

Usage

bertoluzza(X, Y, theta = 1/3, pic = 0)

Arguments

X

...dataframe (polygonal fuzzy number)

Y

...dataframe (polygonal fuzzy number)

theta

...numeric and >0

pic

...numeric, if pic==1 X and Y are plotted, by default no plot is produced.

Details

See examples

Value

...in case X and Y are in the correct form the code returns the Bertoluzza distance, otherwise NA is returned.

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)

Wolfgang Trutschnig <[e-mail]>, Asun Lubiano <[e-mail]>

References

[1] Trutschnig, W., Gonzalez-Rodriguez, G., Colubi, A., Gil, M.A.: A new family of metrics for compact, convex (fuzzy) sets based on a generalized concept of mid and spread, Information Sciences, 179(23), pp. 3964-3972 (2009)

[2] Bertoluzza, C., Corral, N., Salas, A.: On a new class of distances between fuzzy numbers, Mathware Soft Comput., 2, pp:71-84 (1995)

See Also

See Also as checking, Mmean, Bvar

Examples

#Example 1:
data(XX)
X<-translator(XX[[1]],50)
Y<-translator(XX[[2]],50)
Z<-translator(XX[[3]],50)
ZZ<-list(X,Y,Z)
b<-bertoluzza(X,Y,1/3,1)
b

#Example 2: example (SLLN for the FRV)
V<-translator(XX[[3]],100)
YY<-vector("list",length=50)
  for(i in 1:50){
   YY[[i]]<-generator(V,,,)
   }
M<-Mmean(YY)
head(M)
b<-bertoluzza(M,V,1/3,1) 
b

#Example 3:
V<-translator(XX[[3]],100)
YY<-vector("list",length=1000)
  for(i in 1:1000){
   YY[[i]]<-generator(V,,,)
   }
M<-Mmean(YY)
head(M)
b<-bertoluzza(M,V,1/3,1)  
b

#Example 4:
X<-data.frame(x=c(0,1,1,2),alpha=c(0,1,1,0))
Y<-data.frame(x=c(0,1,2),alpha=c(0,1,0))
b<-bertoluzza(X,Y,1/3,1)
b

#Example 5:
data(Trees)
X<-Mmean(Trees[[1]])
Y<-Mmean(Trees[[2]])
Z<-Mmean(Trees[[3]])
b1<-bertoluzza(X,Y,1)
b1
b2<-bertoluzza(X,Z,1)
b2
b3<-bertoluzza(Y,Z,1)
b3