Fuzzy Sets pp 13-24 | Cite as

Minkowski Functionals of L-Fuzzy Sets

  • Ulrich Höhle


The Minkowski functional or gauge of an ordinary set plays an important part in several areas of mathematics, e.g. in the theory of locally convex spaces, optimization, etc. The aim of this paper is to introduce the concept of Minkowski functionals also in the case of L-fuzzy sets. We establish the theorem that there exists a bisection from the set of all absolutely convex, closed, L-fuzzy O-neighborhoods onto the set of all fuzzy continuous, L-probabilistic semi-norms (see Section B).


Aequationes Math Complete Boolean Algebra MINKOWSKI Functional Fuzzy Topology Fuzzy Topological Space 
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Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • Ulrich Höhle
    • 1
  1. 1.Fachbereich MathematikGesamthochschule WuppertalWuppertal 1Federal Republic of Germany

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