Different types of approximation operators on Gn-CAS via ideals

Abstract

A mathematical approach to dealing with the problems of ambiguity and indeterminacy in knowledge is called a rough set theory. It begins by using an equivalence relation to divide the universe into parts. Numerous generalized rough set models have been developed and investigated to increase their adaptability and extend their range of applications. In this context we introduce new generalized rough set models that are inspired by covering-based rough sets and ideals. 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 [2] and Nawar et al.'s method [22] are given. A practical example is given to illustrate one of our methods is more precise.