The further investigation of covering-based rough sets: Uncertainty characterization, similarity measure and generalized models

The superiority of three-way decisions in probabilistic rough set models

“…For example, an equivalence class is in the positive region if and only if it is fully contained in the set. To resolve this problem, probabilistic rough set models have been proposed and studied as generalizations of Pawlak rough sets [16,19,21,28,29,31,34,37,38,43]. Mathematically, one may introduce a probability function on an r-algebra of subsets of a universal set to construct a probabilistic approximation space, within which relationships between concepts can be defined in probabilistic terms [16,28,29,37,38].…”

On measurements of covering rough sets based on granules and evidence theory

“…Compared with the research on covering approximation operators, less efforts have been made on measurements of covering rough sets [40,16,1,19,72] within a unified framework. Shi and Gong [40] defined rough entropy and the granulation of covering for the purpose of measuring the uncertainty of a covering in the covering approximation space, in which the granulation of covering represents the ability of classifications.…”

“…Shi and Gong [40] defined rough entropy and the granulation of covering for the purpose of measuring the uncertainty of a covering in the covering approximation space, in which the granulation of covering represents the ability of classifications. Hu et al [16] investigated the uncertainty measurement of covering rough sets in a Pawlak's approximation space.…”

Applications of repeat degree to coverings of neighborhoods

“…Many scholars [1-3, 22, 23, 46] have done deep researches on this theory. Recently, covering-based rough set theory gained some new development [6,7,26,36,39,42].…”