Generating topologies for attribute-value tables using lattices and neighborhoods

The values in information tables are responsible for dividing the objects of space into partition of object space, which may be topologically. This partition forms a base for topology in complete information system and a subbase for incomplete information systems depending on the arrangement data. The values in information system are responsible for generated different topologies according to the relationship between objects and attributes, since the value is the connection between them. The effectiveness of values in information tables is that the values generate the equivalence classes for a Pawlak approximation space in complete information system, where every equivalence class is a subset of objects and has the same properties. Moreover, attribute values are the primary method for forming these equivalence classes of the approximation space, and the collecting data may take a lot of time, money, and power. If the data does not provide a good analysis, then the effort is wasted and we lose money and time. Therefore, we want to benefit of the data, and change the type of values into another form to generalize of the approximate space. The main aim of this paper was to solve some problems related to values in information system tables by unimportant data reduction due to the structure and types of topologies. On the other hand, the formation of objects lattice for space elements through topological concepts was used. In the new approximation space, the undefinable rough sets changed into definable rough sets depending on new equivalence classes for a Pawlak approximation space through changing the values in information table.