In ‎this ‎paper, ‎we ‎study ‎the ‎relation ‎between ‎the ‎soft ‎sets ‎and ‎soft ‎Lie ‎algebras ‎with ‎the ‎lattice theory. ‎We ‎introduce ‎the ‎concepts ‎of ‎the ‎lattice ‎of ‎soft ‎sets, ‎full ‎soft ‎sets ‎and ‎soft ‎Lie ‎algebras ‎and next, we ‎verify ‎some ‎properties ‎of ‎them. We ‎prove ‎that ‎the ‎lattice ‎of ‎the ‎soft ‎sets ‎on ‎a fixed parameter set is isomorphic to the power set of a ...

The aim of this paper is to initiate and investigate new soft sets over semihypergroups, named special soft sets and transitive soft sets and denoted by $S_{H}$ and  $T_{H},$ respectively. It is shown that $T_{H}=S_{H}$ if and only if $beta=beta^{*}.$ We also introduce the derived semihypergroup from a special soft set and study some properties of this class of semihypergroups.

If σ is a topology on X and A ⊆ X, we let 〈σ,A〉 denote the topology generated by σ and A, i.e., the topology with σ ∪ {A} as a subbasis. Any refinement of a topology obtained like this – by declaring just one new set to be open – we call simple. The present paper investigates the preservation of various properties in simple refinements. The locally closed sets (sets open in their closure) play ...

The aim of this article is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion of union-soft sets is introduced, and its application to BCK/BCI-algebras is considered. The notions of union-soft algebras, union-soft (commutative) ideals and closed union-soft ideals are int...

Abstract In this paper weaker and stronger forms of fuzzy b-mappings are introduced and studied using the concept of fuzzy generalized b-closed sets which are named as fagb-continuous, fagb-irresolute and fagb-closed maps. Also fgbT ∗ 1/2 spaces, fuzzy b-locally closed sets, fb-homeomorphisms, fb*-homeomorphisms, fgb-neighbourhood and fgbq-neighbourhood are introduced and studied. Several inter...