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Statistical Methods for Fuzzy Data by Reinhard Viertl

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23.1 Support functions of fuzzy quantities

Let || · || denote the Euclidean norm, and Sn − 1 = {un: ||u || = 1} the unit sphere, and ·, · the inner product in n. Then each nonempty compact and convex subset An is characterized by its support function

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An element an belongs to the set A if and only if u, asA(u) for all uSn − 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 by

(23.1)

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