Some More Properties of Covering Based Pessimistic Multigranular Rough Sets

Rough sets introduced by Pawlak as a model to capture impreciseness in data is unigranular from the granular computing point of view. In their attempts to introduce multigranulation using rough sets, two models called optimistic multigranular rough sets and pessimistic multigranular rough sets were introduce by Qian et al. in 2006 and 2010 respectively. It is well known that there are several extensions of the basic rough sets to make it more applicable and covering based rough set approach is one among them. Recently, the concept of multigranularity has been extended by Liu et al. to introduce four types of covering based optimistic multigranular rough sets (CBOMGRS). Later, Tripathy et al. introduced the notion of Covering Based Pessimistic Multigranular Rough Sets (CBPMGRS) and proved some of their properties. The important observation is that some of the properties of basic rough sets, which were not true for CBOMGRS, are true for CBPMGRS. So, CBPMGRS seems to be more natural extension of the basic concept than CBOMGRS. Recently Chai has shown that many of the results established by Liu et al. are incorrect, which they rectified. In our results in this paper, we analyse the same for CBPMGRS and incorporate the changes and establish some more properties of CBPMGRS.