On the regularities of fuzzy set multifunctions with applications in variation, extensions and fuzzy set-valued integrability problems

In this paper, we continue our studies concerning regularity. In this sense, we obtain extension results by preserving regularity and we establish basic properties and continuity properties for the variation of fuzzy set multifunctions. This enables us to get relationships among different types of regularity and also to point out regularity properties of the fuzzy set-valued integral .