On Reduction of Morphological Covering Rough Sets

Relationship between generalized rough sets based on binary relation and covering

“…Li studied covering-based rough sets through topological methods [10]. Deng et al used covering-based rough sets to study morphological operators in digital topology [7]. Zhu and Wang did systematic research on five types of covering-based rough sets [50,[52][53][54][55][56]58,60,62].…”

On axiomatic characterizations of three pairs of covering based approximation operators

“…However, the requirement of the equivalence relation in the Pawlak's rough set model seems to be a very restrictive condition that may limit the application domain of the rough set model. To solve this problem, many authors have generalized the notion of approximation operators by using more general binary relations [4,25,26,35,36] or by employing coverings [1][2][3]8,34,41,[45][46][47][48]. Moreover, rough sets can also be generalized into the fuzzy environment and the results are called rough fuzzy sets and fuzzy rough sets [9,10,14,15,23,24,[28][29][30][31][32].…”

A novel roughness measure based on knowledge granulation

“…In the last few decades, many extensions of rough sets have been proposed and the relations between rough sets, fuzzy sets, and concept lattices have been extensively studied [3], [4]. Rough set theory, as a new mathematical tool to deal with inexact, uncertain or vague knowledge, has been drawing wide attention to theoretical research and has become a popular mathematical framework in artificial intelligence, pattern recognition, data mining, intelligence information processing, decision support, image processing, feature selection, conflict analysis, knowledge discovery [2], [5], and so on.…”