SAFD (version 0.3)

DSfrequency: Levelwise Dempster-Shafer frequency

Description

Given a sample XX of polygonal fuzzy numbers and an interval IV the levelwise Dempster-Shafer frequency of the interval is calculated, i.e. for the chosen number nl of equidistant alpha-cuts it is checked how many of the elements of the sample have an alpha-cut that is contained in the interval (lower frequency) and how many have an alpha-cut hitting the interval (upper frequency). These family of intervals is afterwards aggregated to another polygonal fuzzy number with the corresponding number of alpha-cuts, which is returned. For details see [1] below. Preliminary the input data is tested for the correct format using the checking function.

Usage

DSfrequency(XX, IV = c(0, 1), pic = 1, nl = 101)

Arguments

XX

...list of polygonal fuzzy numbers (the functions implicitly checks the conditions)

IV

...numeric vector of length two, by default IV=c(0,1)

pic

...numeric, in case pic=1 the frequency is plotted, otherwise no plot is produced

nl

...number of equidistant alpha-levels, by default nl=101

Value

• Given correct input data, the function returns the levelwise Dempster-Shafer frequency of the chosen interval (again in the correct form of a polygonal fuzzy number).

Details

See examples

References

[1] Trutschnig, W., A strong consistency result for fuzzy relative frequencies interpreted as estimator for the fuzzy-valued probability, Fuzzy Sets and Systems, Vol. 159, nr 3, pp. 259-269 (2008) [2] Viertl, R., Hareter, D.: Beschreibung und Analyse unscharfer Information: Statistische Methoden fuer unscharfe Daten, Springer Wien New York, 2006

See Also

See Also as DShistogram

Examples

# Example 1:
data(XX)
V<-XX[[1]]
SS<-vector("list",length=500)
for (j in 1:500){
 SS[[j]]<-generator(V,)
 }
A<-DSfrequency(SS,c(1,3),1,100)
head(A)