Maximal rough neighborhoods with a medical application

Area of Science:

• Rough Set Theory
• Neighborhood Systems
• Data Analysis

Background:

• Traditional rough set theory relies on equivalence relations or general neighborhood structures.
• Existing neighborhood concepts may not fully capture the nuances required for specific approximation tasks.
• The need for refined approximation methods in data analysis and classification is evident.

Purpose of the Study:

• To introduce and investigate novel maximal neighborhoods, termed $$-neighborhoods.
• To define new $$-lower and $$-upper approximations based on these $$-neighborhoods.
• To evaluate the properties and effectiveness of these new approximations and accuracy measures, including a medical application.

Main Methods:

• Definition and exploration of properties of $$-neighborhoods.
• Application of $$-neighborhoods to define novel lower and upper approximations.
• Analysis of preserved properties of Pawlak's approximations and monotonic properties of accuracy measures.
• Comparative analysis of approximation and accuracy measures under varying $$ values.
• Implementation of a medical application for COVID-19 infection classification.

Main Results:

• Established properties of $$-neighborhoods and their relationship with existing neighborhood types.
• Demonstrated that $$-approximations preserve certain Pawlak properties while others are modified.
• Proved that $$-accuracy measures maintain monotonicity under arbitrary relations.
• Identified optimal approximations and accuracy when $$.
• Successfully applied $$-neighborhoods to classify COVID-19 infection status.

Conclusions:

• The proposed $$-neighborhoods offer a valuable extension to rough set theory, providing enhanced approximation capabilities.
• These new methods demonstrate practical utility, particularly in medical data classification tasks like COVID-19 assessment.
• Further research into the strengths and limitations of this technique compared to existing methods is warranted.