Topological reduction of information systems

The main task of the present work is to apply some methods for knowledge reductions in the case of knowledge based on equivalence relations. Topological techniques are applied to construct knowledge bases via general relations. Topological structures are used to obtain discernibility matrix and discernibility function for knowledge reduction and decision making. Topology plays a significant role in quantum physics, high energy physics, and superstring theory. Reduction of attributes can be applied in the process of compactification of space time dimensions.