frequency {SAFD}R Documentation

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

frequency(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

Details

See examples

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). In case of wrong input data, 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 <wolfgang.trutschnig@softcomputing.es>, Asun Lubiano <lubiano@uniovi.es>

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 histogram

Examples

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

[Package SAFD version 0.02 Index]