Different Types of Approximation Operators on $\complement_n$-CAS via Ideals

Abstract

In this paper, lower and upper approximations of new types of covering rough sets based on $j$-neighborhoods, complementary $j$-neighborhoods, and $j$-adhesions are defined via ideals. The main features of these approximations are examined. The relationships among them are given by various examples and propositions. Some comparisons between our methods and others' methods such as Abd El-Monsef et al.'s method \cite{Abd El} and Nawar et al.'s method \cite{Nawar} are given. A practical example is given to illustrate one of our methods is more precise.