4
Fuzzy samples
Fuzzy samples consist of a finite sequence of fuzzy numbers, i.e. x1*,…xn*, or a finite sequence of fuzzy vectors x1*,…xn*. In this chapter the concepts of minimum and maximum of observations are extended to fuzzy samples. Moreover generalized cumulative sums are introduced.
4.1 Minimum of fuzzy data
Let x1*,…xn* be n fuzzy intervals whose corresponding δ-cuts are denoted by Cδ(xi*) = [
δ,i,
δ,i] for δ ∈ (0; 1] and i = 1(1)n. The fuzzy valued minimum min{x1*,…xn*} is a fuzzy interval xmin* whose δ-cuts Cδ(xmin*) are defined by
The characterizing function of xmin* is obtained by (the representation) Lemma 2.1.
4.2 Maximum of fuzzy data
Under the same conditions as in Section 4.1 the maximum of n fuzzy intervals x1*,…xn* is the fuzzy interval xmax* = max{x1*,…xn*} whose δ-cuts Cδ(xmax*) are defined by
Remark 4.1:
The minimum as well as maximum of fuzzy intervals reduce to the classical minimum and maximum for classical samples x1,…,xn.
Examples are given in Section 4.4.
4.3 Cumulative sum for fuzzy data
In the case of classical samples x1,…,xn with xi ∈ of one-dimensional ...
