Ideal-Based Rough Approximations: Python Implementation and School-Selection Verification

Abstract

This software provides a Python implementation of refined ideal-based rough approximation operators associated with generalized neighbourhood systems. The package includes: A Python implementation of classical and refined ideal-based lower and upper approximations, positive, boundary, and negative regions, and approximation accuracy. A reproducible school-selection example involving incomplete information and directional attribute-wise neighbourhoods. An independent verification suite covering 4,096 school-subset and principal-ideal combinations, 2,000 randomized generalized-neighbourhood cases, all 30 attribute-wise neighbourhood calculations, and additional edge cases. The software uses only the Python standard library and was successfully tested on Windows using Python 3.14. Related research publication: Zakaria, A., El-Sheikh, S., Mohamed, S., and Said, E. (2026). Ideal-Based Rough Approximations: Algorithms and Applications for Incomplete Data. Turkish Journal of Mathematics and Computer Science, 18(3), 639–655. https://doi.org/10.47000/tjmcs.1813065 Scope: This release implements the refined ideal-based approximation algorithms and computational examples associated with Chapter 2 of the related thesis. It does not implement the neighbourhood-kernel membership algorithms of Chapter 3.