Abstract

Puri and Ralescu (1985) gave, recently, an extension of the Minkowski Embedding Theorem for the class double-struck E signn L of fuzzy sets u on ?n with the level application ? ? L?u Lipschitzian on the C([0, 1] × Sn-1) space. In this work we extend the above result to the class double-struck E signn C of level-continuous applications. Moreover, we prove that double-struck E signn C is a complete metric space with double-struck E signn L??double-struck E signn C and double-struck E signn L = double-struck E signn C. 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). © 1999 Elsevier Science B.V. All rights reserved.