Regarding the study of digital topological rough set structures, the present
paper explores some mathematical and systemical structures of the
Marcus-Wyse (MW-, for brevity) topological rough set structures induced by
the locally finite covering approximation (LFC-, for brevity) space (R2,C)
(see Proposition 3.4 in this paper), where R2 is the 2-dimensional Euclidean
space. More precisely, given the LFC-space (R2,C), based on the set of
adhesions of points in R2 inducing certain LFC-rough concept approximations,
we systematically investigate various properties of the MW-topological rough
concept approximations (D -M, D+M) derived from this LFC-space (R2,C).
These approaches can facilitate the study of an estimation of roughness in
terms of an MW-topological rough set. In the present paper each of a
universe U and a target set X(? U) need not be finite and further, a
covering C is locally finite. In addition, when regarding both an M-rough
set and an MW-topological rough set in Sections 3, 4, and 5, the universe
U(? R2) is assumed to be the set R2 or a compact subset of R2 or a certain
set containing the union of all adhesions of x ? X (see Remark 3.6).
Characterizations of an MW-topological rough set structure
