A topological approach for improving accuracy in decision-making via bi-ideal approximation

The present paper proposes a novel version of inducing nano topology by using new kinds of approximation operators via two ideals with respect to a general binary relation. This approach improves the accuracy of the approximation quite significantly. These newly defined approximations constitute the generalized version of rough sets defined by Pawlak in 1982. A comparison is drawn between the suggested technique and the already existing ones to demonstrate the significance of the proposed ideology. In addition, the standard notion of nano topology, based on an equivalence relation is generalized to the binary relation, which can have a broader scope when applied to intelligent systems. Also, the significance of this approach is demonstrated by an example where an algorithm is given to find the key factors responsible for the profit of a company along with the comparison to the previous notions. Likewise, the proposed algorithm can be used in all fields of science to simplify complex information systems in extracting useful data by finding the core.