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Type: Artigo de periódico
Title: A generalization of the Minkowski embedding theorem and applications
Author: Rojas-Medar, M
Bassanezi, RC
Roman-Flores, H
Abstract: Purl and Ralescu (1985) gave, recently, an extension of the Minkowski Embedding Theorem for the class E-L(n) of fuzzy sets u on R-n with the level application alpha --> L(alpha)u Lipschitzian on the C([0, 1] x Sn-1) space. In this work we extend the above result to the class E-C(n) of level-continuous applications. Moreover, we prove that E-C(n) is a complete metric space with E-L(n) not subset of or equal to E-C(n) and <(E-L(n))over bar> = E-C(n). To prove the last result, we use the multivalued Bernstein polynomials and the Vitali's approximation theorem for multifunction. Also, we deduce some properties in the setting of fuzzy random variable (multivalued). (C) 1999 Elsevier Science B.V. All rights reserved.
Subject: fuzzy sets
Hausdorff metric
integration of multifunctions
multivalued Bernstein polynomial
Minkowski Embedding Theorem
support functions
Country: Holanda
Editor: Elsevier Science Bv
Rights: fechado
Identifier DOI: 10.1016/S0165-0114(97)00120-6
Date Issue: 1999
Appears in Collections:Artigos e Materiais de Revistas Científicas - Unicamp

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