The Lattice Structure of Coverings in an Incomplete Information Table with Value Similarity

Abstract

AbstractBased on Lipski’s approach dealing with incomplete information tables, we describe lower and upper approximations using coverings under incomplete information and similarity of values. Lots of coverings, called possible coverings, on a set of attributes are derived in an incomplete information table with similarity of values, although the covering is unique in a complete information table. The family of possible coverings has a lattice structure with the minimum and maximum elements. This is true for the family of maximal descriptions, but is not for the family of minimal descriptions and the family of 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. Therefore, there is no difficulty of the computational complexity in our approach.KeywordsRough setsIncomplete informationPossible coveringsPossibly indiscernible classesLower and upper approximations