What is it about?

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.

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Why is it important?

The motivation of this study is that this concept can be used to determine a decision based on multiple opinions, rather than one. Also, the main advantage of this ideology is that the accuracy using this approach is significantly greater than the already existing ones. As the bi-ideal approach assimilates together the notion of combined opinions through two ideals, it can further be generalized to `n' ideals (`n' opinions) and hence a mathematical model can be designed to study the interdependence of various factors and various situations, which arise in fields of physics, chemistry, and biology. This approach can help in simplification and easy interpretation of any information system by removing unwanted data. Hence, it can contribute a lot to studying the qualitative and quantitative properties of various elements, compounds, and species. This study has a great scope in medicine, biochemistry, and engineering.


This paper extends the idea of approximation via a single ideal to two ideals, which may further be generalized to any finite no. of ideals, which can help in framing an algorithm to deal with condition attributes and decision attributes via a collaborated viewpoint of multiple opinions. A study on its range of applications is currently in progress.

Kamalpreet Kaur
Punjab Engineering College (Deemed to be university), Chandigarh, India, 160012

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This page is a summary of: A topological approach for improving accuracy in decision-making via bi-ideal approximation, Journal of Intelligent & Fuzzy Systems, March 2023, IOS Press, DOI: 10.3233/jifs-222958.
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