Boolean Algebra of Soft Q-Sets in Soft Topological Spaces. (28th August 2022)

• Record Type: Journal Article
• Authors: Al Ghour, Samer
• Other Names: V. E. Sathishkumar Academic Editor.
• Is Part Of: Applied computational intelligence and soft computing. Volume 2022(2022)
• Publication Date: 2022-08-28
• Subjects: Computational intelligence -- Periodicals; Soft computing -- Periodicals; 006.305
• DOI: 10.1155/2022/5200590
• Languages: English
• ISSNs: 1687-9724

Abstract

Abstract : We define soft Q -sets as soft sets whose soft closure and soft interior are commutative. We show that the soft complement, soft closure, and soft interior of a soft Q -set are all soft Q -sets. We show that a soft subset K of a given soft topological space is a soft Q-set if and only if K is a soft symmetric difference between a soft clopen set and a soft nowhere dense set. And as a corollary, the class of soft Q -sets contains simultaneously the classes of soft clopen sets and soft nowhere dense sets. Also, we prove that the class of soft Q -sets is closed under finite soft intersections and finite soft unions, and as a main result, we prove that the class of soft Q -sets forms a Boolean algebra. Furthermore, via soft Q -sets, we characterize soft sets whose soft boundaries and soft interiors are commutative. In addition, we investigate the correspondence between Q -sets in topological spaces and soft Q -sets in soft topological spaces.