Lattice Structures Related with Rough Sets in an Incomplete Information Table with Value Similarity

Abstract

The family of possible coverings and a family of possible indiscernibility relations have a lattice structure with the minimum and maximum elements. This is true for the family of possible maximal descriptions, but is not for the family of possible minimal descriptions and the family of possible sets of close friends. As was shown by Lipski, what we can obtain from an information table with incomplete information is the lower and upper bounds of information granules. Using only two coverings: the minimum and maximum possible ones, we obtain the lower and upper bounds of lower and upper approximations. There, therefore, exists no difficulty of the computational complexity in our approach.