Topological Rough Algebras

On Covering Rough Sets

“…It is noticed that equivalence relation or partition, as the indiscernibility relation in Pawlak's original rough set theory, is restrictive for many applications. To address this issue, several interesting and meaningful extensions to equivalent relation have been proposed in the past, such as tolerance relation [4,12], similarity relation [13], and others [14,15,16,17]. This leads to various approximation operators.…”

Measuring roughness of generalized rough sets induced by a covering

“…But, partition or equivalence relation is still restrictive for many applications. To address this issue, several interesting and meaningful extensions to equivalence relation have been proposed in the past, such as tolerance relations [7,15], similarity relations [16], others [17][18][19]. Particularly, Zakowski has used coverings of an universe for establishing the generalized rough set [21].…”

Rough 3-valued algebras

“…Banerjee and Chakraborty [2] proposed an algebraic structure called rough algebra while studying rough equality within the framework of the modal system S 5 . In the subsequent research, Banerjee and Chakraborty [3] noticed that the so-called rough algebra is a particular case of topological quasi-Boolean algebra which was formalized in [37]. In a topological Boolean algebra, the laws of contradiction and exclude middle fail to hold.…”

“…There have been extensive studies on the rough set theory by algebraic methods [1][2][3][33][34][35][37][38][39][40][41][42]. Wong and Nie [38] and Wong et al [39], proposed a generalization of the notion of rough sets under interval structures.…”