Approximation Distance Calculation on Concept Lattice

The heart of the extended rough set theory is the generalization of the notion of the standard set inclusion degree. Considering the equivalent relationship between equivalence class in rough set theory and concept in concept lattice, we will study a classification problem of undefinable object set (undefinable object set is the object set that is not an extension) in concept lattice. First, with the definition of inclusion degree, we propose a definition of approximation distance. Second, we introduce an algorithm to vectorize a set. Third, in a context, with the assistance of the algorithm above, we find out an algorithm to calculate a closest extension to an undefinable object set. We also use an example to illustrate the feasibility of this algorithm. Finally, we conclude this paper and point out the future works.