Topological operators of MW -topological rough approximations

摘要

The present paper focuses on the studies of the topological (interior and closure) operators of the M-rough set structure (M-*, M*) and the Marcus-Wyse (MW-, for brevity) topological rough set structure (D-M(-), D-M(+)). While the concept approximations (M-*, M*) are topological operators, it is well known that the function D-M(-) is not an interior operator and D-M(+) is not a closure one either. Hence an issue can be posed as follows: What condition makes D-M(-) (resp. D-M(+)) an interior (resp. a closure) operator? This paper proposes a new frame addressing the issue, the so-called (Delta(-)(M), Delta(+)(M)) instead. This new version smoothly matches with (M-*, M*) w.r.t. the topological operators. Furthermore, both (M*, M*) and (Delta(-)(M), Delta(+)(M)) are shown to have many theoretical and mathematical properties in common. Therefore, they can efficiently be used in applied sciences with a strong combination. Besides, they can support certain decision rules without any limitations of studying something continuous or discrete (or digital) from the viewpoint of covering rough set theory. In this paper each of a universe U and a target set X of U need not be finite, and a covering Cis locally finite. (C) 2020 Elsevier Inc. All rights reserved.