Soft Atoms and Soft Complements of Soft Lattices

Soft set theory was introduced by Molodtsov in 1999 as a mathematical tool for dealing with problems that contain uncertainty. Faruk Karaaslan et al.[6] defined the concept of soft lattices, modular soft lattices and distributive soft lattices over a collection of soft sets. In this paper, we define the concept of complemented soft lattices and complemented distributive soft lattices over a collection of soft sets, study their related properties and illustrate them with some examples. We also define the concept of soft Boolean algebras, soft atoms of soft lattices and discuss the theorems related to soft atoms. In addition, we establish representation theorem for finite soft Boolean algebras.