This paper deals with approaches to the granular space reductions in the variable precision multigranulation rough set model. The main objective of this study is to extend four kinds of the granular space reductions called a tolerance relations optimistic multigranulation  ower approximation distribution reduction, a tolerance relations optimistic multigranulation  upper approximation distrib...

The optimistic multigranulation T-fuzzy rough set model was established based on multiple granulations under T-fuzzy approximation space by Xu et al., 2012. From the reference, a natural idea is to consider pessimistic multigranulation model in T-fuzzy approximation space. So, in this paper, the main objective is to make further studies according to Xu et al., 2012. The optimistic multigranulat...

The classical multigranulation rough set (MGRS) theory offers a formal theoretical framework for solving the complex problem under multigranulation environment. However, it is noticeable that MGRS theory cannot be applied in multi-source information systems with a covering environment in the real world. To address this issue, we firstly present in this paper three types of covering based multig...

Multigranulation rough set theory is a relatively new mathematical tool for solving complex problems in the multigranulation or distributed circumstances which are characterized by vagueness and uncertainty. In this paper, we first introduce the multigranulation approximation space. According to the idea of fusing uncertain, imprecise information, we then present three uncertainty measures: fus...

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 re...

For further studying the theory of multigranulation rough sets (MGRS), we attempt to investigate a new theory on multigranulation rough sets from the topological view in this paper. We firstly explore multigranulation topological rough space and its topological properties by giving some new definitions and theorems. Then, topological granularity and topological entropy are proposed to character...

Multigranulation rough sets are desirable features in the field of rough set, where this concept is approximated by multiple granular structures. In this study, we employ belief and plausibility functions from evidence theory to characterize the set approximations and attribute reductions in multigranulation rough set theory. First, we show that in an incomplete information system, the pessimis...

In this paper, we mainly investigate the equivalence between multigranulation approximation space and single-granulation approximation space from the lattice-theoretic viewpoint. It is proved that multigranulation approximation space is equivalent to single-granulation approximation space if and only if the pair of multigranulation rough approximation operators [Formula in text] forms an order-...

The decision-theoretic rough set model based on Bayesian decision theory is a main development tendency in the research of rough sets. To extend the theory of decision-theoretic rough set, the article devotes this study to presenting multigranulation decision-theoretic rough set model in ordered information systems. This new multigranulation decision-theoretic rough set approach is characterize...

The multigranulation rough set (MGRS) is becoming a rising theory in rough set area, which offers a desirable theoretical method for problem solving under multigranulation environment. However, it is worth noticing that how to effectively extract decision rules in terms of multigranulation rough sets has not been more concerned. In order to address this issue, we firstly give a general ruleextr...