23
Mathematical concepts
In this chapter mathematical concepts will be described which are used later in this part.
23.1 Support functions of fuzzy quantities
Let || · || denote the Euclidean norm, and Sn − 1 = {u ∈ 
n: ||u || = 1} the unit sphere, and 
·, ·
the inner product in n. Then each nonempty compact and convex subset A ⊆ n is characterized by its support function
An element a ∈ n belongs to the set A if and only if u, a ≤ sA(u) for all u ∈ Sn − 1.
By a specialization of Definition 2.3 the δ-cuts of a fuzzy vector x* ∈ F(n) are compact and convex subsets of n. Therefore x* is characterized ...
