Multigranulation decision-theoretic rough sets in incomplete information systems

Abstract

We study multigranulation decision-theoretic rough sets in incomplete information systems. Based on Bayesian decision procedure, we propose the notions of weighted mean multigranulation decision-theoretic rough sets, optimistic multigranulation decision-theoretic rough sets, and pessimistic multigranulation decision-theoretic rough sets in an incomplete information system. We investigate the relationships between the proposed multigranulation decision-theoretic rough set models and other related rough set models. We also study some basic properties of these models. We give an example to illustrate the application of the proposed models.

Updating knowledge in multigranulation decision‐theoretic rough set model based on decision support degree

“…Considering the rough set may be associated with multiple granular structures in practical application, Qian et al [13] extended the single granulation rough set model to the multigranulation rough set model. And then, many extended multigranulation rough set models, the relative properties and applications, have also been researched [14–21]. Qian et al [22] expanded the decision‐theoretic rough set theory based on the Bayesian decision procedure into the multigranulation perspective.…”

Granularity reduction method based on positive decision holding for multi‐granulation decision‐theoretic rough set

“…Among numerous results of the extended MGRS models, the research of MG‐DTRS is less. Since 2014, Qian et al firstly proposed the framework of MGRS model, some scholars have begun to study the MG‐DTRS [15–20]. Yang and Guo [15] analysed the MG‐DTRSs in incomplete information systems, Xu and Guo [17] proposed an MG‐DTRS model based on covering, and Liu et al [20] studied MG‐DTRSs from a local perspective, but in the above literature, the granular structure selection problem on MG‐DTRS model has not been investigated.…”

“…Since 2014, Qian et al firstly proposed the framework of MGRS model, some scholars have begun to study the MG‐DTRS [15–20]. Yang and Guo [15] analysed the MG‐DTRSs in incomplete information systems, Xu and Guo [17] proposed an MG‐DTRS model based on covering, and Liu et al [20] studied MG‐DTRSs from a local perspective, but in the above literature, the granular structure selection problem on MG‐DTRS model has not been investigated. Sang and Qian [18] analysed the granular structure selection problem under multiple granular spaces, and introduced the concept of the approximate distribution reduction to MG‐DTRS model; furthermore, the α‐lower approximate distribution reduction algorithm to obtain a granular structure reduction was designed based on the multiple granular approximate distribution quality.…”

Binary Classification of Multigranulation Searching Algorithm Based on Probabilistic Decision

“…But for millions and even billions of objects, can this kind of single-level granulation method still effectively solve the complex problem? At present, there are lots of methods about the single-level granulation searching model [44][45][46][47][48][49][50][51][52][53][54], but the studies on the multilevels granulation searching model are few [55][56][57][58][59]. A binary classification of multilevels granulation searching algorithm, namely, establishing an efficient multigranulation binary classification searching model based on hierarchical quotient space structure, is proposed in this paper.…”