On the equivalence of convergences of fuzzy sets

Abstract

The aim of this paper is to compare D, H and L-convergences with the variational covergence. Our analysis, which is carried out in ®″, is made through the introduction of the space ϵ c″ of compact fuzzy sets u on ®″, for which the level function α ∃ [0, 1] → L, μ ∃ Π K ( ϵ″) is continuous. We prove that in this space all the above notions of convergence are equivalent.