Comments on "Characteristic matrix of covering and its application to Boolean matrix decomposition[Information Sciences 263(1), 186-197, 2014]"

TL;DR

This paper offers improvements and new insights into the sixth lower and upper approximations in covering approximation spaces, including dual and matrix-based perspectives, refining prior theoretical results.

Contribution

It extends the theory of covering approximation spaces by introducing dual and matrix-based sixth approximations, enhancing understanding and computational approaches.

Findings

Improved Theorem 7 and Example 8 from prior work.

Introduction of sixth dual lower and upper approximations.

Matrix-based construction of the sixth dual approximations.

Abstract

In this note, we show some improvements for Theorem 7 and Example 8 in Shiping Wang[Information Sciences 263(1), 186-197, 2014]. Concretely, we study further the sixth lower and upper approximations of sets for covering approximation spaces. Furthermore, we present the sixth dual lower and upper approximations of sets for covering approximation spaces. We also construct the sixth dual lower and upper approximations of sets from the view of matrix. Throughout, we use the same notations as Shiping Wang[Information Sciences 263(1), 186-197, 2014].