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Research Paper | Mathematics | India | Volume 3 Issue 5, May 2014 | Rating: 6.1 / 10
Soft Atoms and Soft Complements of Soft Lattices
E. K. R. Nagarajan, P. Geetha
Abstract: 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.
Keywords: Soft atoms, soft complements, complemented soft lattices, soft Boolean algebras
Edition: Volume 3 Issue 5, May 2014,
Pages: 529 - 534