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Distributive Lattice: A Rough Set Approach

This paper studies the distributive lattice under the rough set environment and thereby forms a concept of rough distributive lattice. We have discussed the properties of lattice theory in the approximation space and defined rough lattice, rough sublattice and complete rough lattice. We have defined approximation space by using an equivalence relation and then present rough set as a pair of two ordinary sets namely lower and upper approximation sets in the approximation space. The objective of this paper is to study the lattice theory based on rough set by using indiscernibility relation. Some important result are proved. Finally we cite some examples to illustrate the definitions and theories.