New results on type-2 soft sets

Abstract

In this paper, we introduce some new operations on type-2 soft sets and discuss related properties. The notions of primary empty type-2 soft sets, underlying empty type-2 soft sets and complete type-2 soft sets are introduced. In particular, we define four new operations (the extension,the restriction, the extension-restriction, the restriction-extension) each on union, intersection and difference. By using these new definitions we prove certain De Morgan's laws in type-2 soft set theory. Finally, an example which shows the validity of De Morgan's laws in real life problems is presented.