New results on type-2 soft sets

Year 2018, Volume: 47 Issue: 4, 855 - 876, 01.08.2018

Khizar Hayat , Muhammad İrfan Ali , Bing-yuan Cao , Faruk Karaaslan

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.

Keywords

Type-2 soft sets, empty type-2 soft sets, the extension, the restriction, the extension-restriction, the restriction-extension, union, intersection, difference and De Morgan's laws

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