Generalized probabilistic approximations of incomplete data

Editing Training Sets from Imbalanced Data Using Fuzzy-Rough Sets

“…Apart from using equivalence relations to define a rough set in complete information systems, there are also numerous studies [10,13,16,17,18] that deal with incomplete or imperfect information systems in which data are not described by precise and crisp values.…”

Game-theoretic rough sets for recommender systems

“…(9)- (11) is that the decisions of objects belonging to any of the three regions are affected and determined by the choice of thresholds ða; bÞ. Considering making recommendation decisions with the probabilistic rough set model, different recommendations may be possible for the same object when different threshold values are being used.…”

“…The probabilistic rough set models represent one class of these quantitative models and include the decision-theoretic rough set model [40,45], the variable precision rough set model [47,48], the Bayesian rough set model [10,31], the information-theoretic rough set model [9] and the game-theoretic rough set model [12,39]. An important realization in these models is that a pair of thresholds ða; bÞ is used to define the rough set approximations and the resulting three regions [11,41,43] determination and interpretation of thresholds are two important issues in the probabilistic rough sets [43]. Some notable attempts in this regard can be found in references [4,9,12,16,[19][20][21].…”

Mutual information criterion for feature selection from incomplete data

“…Thus the Pawlak information granule is not suitable for incomplete data. To be applicable for incomplete data, two main kinds of information granules are generated as follows [12,40]: tolerance information granules and similarity information granules. Induced by a tolerance relation, the granulation of objects generates a set of tolerance classes, in which each tolerance class can be seen as a tolerance information granule.…”

“…Induced by a tolerance relation, the granulation of objects generates a set of tolerance classes, in which each tolerance class can be seen as a tolerance information granule. Induced by a similarity relation, the granulation of objects generates a set of similarity classes, in which each similarity class can be seen as a similarity information granule [40]. The way in which the granulation of objects generated by a family of the tolerance information granules is representative and extensively studied [3,9,12,16,18,34,35].…”