Generating minimal topologies from  κ -neighborhoods and primals

Rodyna A. Hosny; Mostafa K. El-Bably

doi:10.54517/mss3202

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Quarterly since 2025

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2024

2023

Generating minimal topologies from κ-neighborhoods and primals

Rodyna A. Hosny, Mostafa K. El-Bably

Article ID: 3202
Vol 3, Issue 1, 2025

DOI: https://doi.org/10.54517/mss3202

Received: 3 January 2025; Accepted: 24 February 2025; Available online: 21 March 2025; Issue release: 31 March 2025

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Abstract

This manuscript presents innovative rough approximation operators based on an abstract structure called “minimal topology”. This approach offers greater flexibility than traditional topological frameworks by removing the conventional closure requirements for unions and intersections inherent in standard topology, thereby expanding its applicability. We construct eight types of minimal topologies using N_κ-neighborhood systems and the concept of primals. The relationships between these topologies are examined, with a focus on identifying conditions under which they are equivalent. New rough-set models are derived from these minimal topologies, and key properties of their lower and upper approximations are established. Additionally, we apply these approximations to classify subset regions and compute their accuracy measures.

Keywords

approximation spaces; minimal topology; primal; rough set theory

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