R#-Closed Sets as a Topological Approximation Framework for Attribute Reduction in Data Classification

Raghavendra K; Veeresha A Sajjanara; Govardhanareddy H G

doi:10.36948/ijfmr.2026.v08i05.87687

R#-Closed Sets as a Topological Approximation Framework for Attribute Reduction in Data Classification

Author(s)	Dr. Raghavendra K, Dr. Veeresha A Sajjanara, Dr. Govardhanareddy H G
Country	India
Abstract	Rough set theory approaches uncertainty in classification through topological closure and interior — the operators behind the classical lower and upper approximation of a decision class. Here we ask a narrower question: does a specific generalized closed-set notion from point-set topology, the R#-closed set, buy anything for that construction? R#-closed sets sit strictly between generalized closed (g-closed) sets and regular generalized closed (rg-closed) sets, and that placement turns out to be enough. Because every closed set is g-closed, and every R#-closed set falls in the g-closed/rg-closed interval, the resulting R#-closure can only shrink the classical upper approximation, and R#-interior can only grow the classical lower approximation. The boundary region shrinks accordingly, and the accuracy measure can only hold steady or improve. We work this out as an R#-approximation space, prove the tightening result, build an attribute-reduction procedure on top of it, and walk through the mechanics on a small decision table. What emerges is a modest but mathematically solid connection between generalized-closed-set topology and rough-set-based feature reduction — the kind of bridge that is easy to state once you see it, but had not, to our knowledge, been made before.
Keywords	R#-closed sets; generalized topology; rough sets; topological approximation space; attribute reduction; data classification.
Field	Mathematics
Published In	Volume 8, Issue 5, September-October 2026
Published On	2026-09-20
DOI	https://doi.org/10.36948/ijfmr.2026.v08i05.87687

View / Download PDF File

About IJFMR Fees & Payment Current Issue Publication Archive	Submit Research Paper Track Submission Status Publication Guidelines Publication Ethics Peer Review & Plagiarism	Join as a Reviewer Editors & Reviewers Reviewer Referral Program Get Reviewer Membership Certi.	Website/Journal Policies Usage Policy Content Policies Privacy Policy

Contact Us		+91-9687-828-838	editor@ijfmr.com

International Journal For Multidisciplinary Research

A Widely Indexed Open Access Peer Reviewed Multidisciplinary Bi-monthly Scholarly International Journal

R#-Closed Sets as a Topological Approximation Framework for Attribute Reduction in Data Classification

Share this