New results on type-2 soft sets

Authors : Khizar HAYAT, Muhammad İrfan ALİ, Bing-yuan CAO, Faruk KARAASLAN

Pages : 855-876

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Publication Date : 2018-08-01

Article Type : Research Paper

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 insert ignore into journalissuearticles values(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