An embedding theorem for convex fuzzy sets

Authors:
Pedro Terán
Affiliations:
Facultad de Ciencias Económicas y Empresariales, Departamento de Métodos Estadísticos, Universidad de Zaragoza, Gran Vía, 2. E-50005 Zaragoza, Spain
Venue:
Fuzzy Sets and Systems
Year:
2005

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Abstract

In this paper we embed the space of upper semicontinuous convex fuzzy sets on a Banach space into a space of continuous functions on a compact space. The following structures are preserved by the embedding: convex cone, metric, sup-semilattice. The indicator function of the unit ball is mapped to the constant function 1. Two applications are presented: strong laws of large numbers for fuzzy random variables and Korovkin type approximation theorems.