5

Histograms for fuzzy data

Classical histograms are based on precise data x1,…,xn in order to explain the distribution of the observations xi. In order to construct histograms the set M of possible values xi is decomposed into so-called classes K1,…,Kk with Ki ∩ Kj = ∀i ≠ j, and

Then for each class Kj the so-called relative frequency hn(Kj) is calculated, i.e.

The display of the relative frequencies is called a histogram.

For fuzzy data the following problem arises: By the fuzziness of observations it is not always possible to decide in which class Kj a fuzzy observation x* with characterizing function ξ(·) lies. This is depicted in Figure 5.1.

Therefore a generalization of histograms is necessary.