Defuzzification using Steiner points

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Mirko Navara
Thomas Vetterlein
Title: Defuzzification using Steiner points
Journal: Fuzzy Sets and Systems
Volume 157
Pages: 1455 - 1462
Year: 2006


A defuzzification function assigns to each fuzzy set a crisp value in a way that this value may intuitively be understood as the "centre" of the fuzzy set.

In the present paper, this vague concept is put into a mathematically rigorous form. To this end, we proceed analogously to the case of sharply bordered subsets, for which the Steiner point is frequently used. The function assigning to each convex subset its Steiner point is characterised by three properties; here, we study functions whose domains consist of fuzzy sets and which fulfil analogous properties.

Although uniqueness can no longer be achieved, we give a complete characterisation of what we call Steiner points of fuzzy sets.