On the equivalence of convergences of fuzzy sets

The aim of this paper is to compare D, h and L-convergences with the variational convergence. Our analysis, which is carried out in R(n), is made through the introduction of the space E(c)(n) of compact fuzzy sets u on R(n), for which the level function alpha is an element of [0, 1] --> L(alpha)u is an element of P-K(R(n)) is continuous. We prove that in this space all the above notions of convergence are equivalent.