Topology (electrical circuits)

Closed set

Mathematics

Computer science

Closure (psychology)

Economics

Market economy

Combinatorics

Soft set

Artificial intelligence

Boolean algebra

Fuzzy logic

Discrete mathematics

Commutative property

Topological space

Applied Computational Intelligence and Soft Computing

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.

Boolean Algebra of Soft Q-Sets in Soft Topological Spaces