In this paper, direct proofs of some properties of new classes of fuzzy sets called fuzzy strongly g∗-closed sets and fuzzy g∗∗-closed sets are introduced. Examples are presented showing that some generalizations can not be obtained. MSC: 54A40 • 54A05

Let G be a real semi-simple noncompact Lie group and S ⊂ G a subsemigroup with intS 6= Ø . This article relates the Bruhat-Chevalley order in the Weyl group W of G to the ordering of the control sets for S in the flag manifolds of G by showing that the one-to-one correspondence between the control sets and the elements of a double coset W (S) \W/WΘ of W reverses the orders. This fact is used to...