An application of soft sets to lattices

E. K. R. Nagarajan, G. Meenambigai

Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we initiate the study of soft lattices by using soft set theory. The notions of soft lattices, soft distributive lattices, soft modular lattices, soft lattice ideals, soft lattice homomorphisms are introduced and several related properties and some characterization theorems are investigated.