Covering Approximation Space for Lattice

In 1981 Prof. Pawlak introduced Rough set theory. It covers the areas of research in artificial intelligence, knowledge representation system, imprecision, vagueness and others. All vague concepts is substituted by a pair of precise concepts-one is the lower approximation and other is the upper approximation of the vague concept. The lower approximation consists of all objects which definitely belong to the concept and the upper approximation contains all objects which probably belong to the concept. The difference between these two approximations constitutes the boundary region of the vague concept. Lattice concept was introduced by Peirce and Schroder. Structure of Lattices are simple since the basic concepts of the theory include only least upper bounds, greatest lower bounds and the order relation. Now it plays an important role in many disciplines of engineering and computer science.

Here we applied the rough set theory to the lattice theory and a concept introduced here known as lattice rough, which deals with the problems of uncertainties in our day to day life.