Covering Approximations Approach to Interval Ordered Information Systems

It is been proved that the theory of rough set is very beneficial in working with conflict problems induced by the information endearment The original idea of the rough set is not accurate, however, when preference orders of characteristics domains (standard) are to be considered. Seeking the issue of covering approximation relative to a control relation in interval-ordered information systems is a new mathematical tool to set up a control-based rough set approach. These Mathematical tools apply some topological generalizations, and control relations, covering approximations, and interval information systems. These results using our approach are more accurate than using a classical approach such as the approach of Pawlak. Topologies reproduce types of information systems with one value. By defining a control relation to interval information systems, we generalized the Pawlak approximation space to a covering approximation space and then we involve this approach to work with the interval-ordered information systems. Results gained by the proposed approach to generate two different rough approximations called j-lower and j-upper approximations. We applied j-rough notions such as j-rough membership, j-rough equality, and j-rough inclusion relations using topological generalizations. Our proposed method has improved the results gained from interval information systems. In this Research, there are many improved approaches to investing generalized approximation relative to a control relation in interval information systems, and we use the covering approximation in the rough set approach. This is a generalization of the Pawlak approach applied to interval information systems. This approach opens the way for other generalizations by making new algorithms, which simplify the calculations on it, and we can add more topological concepts to support decision-making in real-life applications.