Defuzzification using Steiner points

Abstract

Keywords

Bibtex entry

@TechReport{Vetterlein-TR-2005-20,
  author =	 {Thomas Vetterlein and Mirko Navara},
  title =	 {Defuzzification using {S}teiner points},
  institution =	 {Center for Machine Perception, K13133 FEE Czech Technical University},
  address =	 {Prague, Czech Republic},
  year =	 {2005},
  month =	 {July},
  type =	 {Research Report},
  number =	 {{CTU--CMP--2005--20}},
  issn =	 {1213-2365},
  annote = {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
    characterized 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 characterization of what we call Steiner points of
    fuzzy sets.},
  keywords =	 {convex set, convex fuzzy set, Steiner point, 
                  center of gravity, defuzzification, 
                  computer vision, medical imaging},
}