On Covering Based Pessimistic Multigranular Rough Sets

Rough sets were introduced by Pawlak as a model to capture impreciseness in data and several techniques in different directions have been developed to perform operations on such data through the model. But the basic model of rough set introduced is unigranular from the granular computing point of view. So, attempts have been made 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. However, like the basic case, the information granules generated were introduced by equivalence relations and as a result the granules are members of partitions induced on the universe. However, such concepts have limited applications due to the rarity of equivalence relations or equivalently partitions of universes. The notion of cover is more general than partition and covers are available in abundance in real life situations. So, even in the case of basic rough sets the definition has been extended to develop covering based rough sets. Recently, the concept of multigranularity has been extended by Liu et al to introduce four types of covering based optimistic multigranular rough sets (CBOMGRS). In this paper we introduce the notion of Covering Based Pessimistic Multigranular Rough Sets (CBPMGRS) and proved some 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 extensions of the basic concepts than CBOMGRS.