Covering-Based Pessimistic Multigranular Approximate Rough Equivalences and Approximate Reasoning

The multigranular rough set (MGRS) models of Qian et al. were extended to put forth covering-based multigranular rough sets (CBMGRS) by Liu et al. in 2012. The equality of sets, which is restrictive and redundant, was extended first in Pawlak (Rough sets: theoretical aspects of reasoning about data. Kluwer, London, 1991) and subsequently in Tripathy (Int J Adv Sci Technol 31:23-36, 2011) to propose four types of rough set-based approximate equalities. These basic concepts of rough equalities have been extended to several generalized rough set models. In this paper, covering-based pessimistic multigranular (CBPMG) approximate rough equivalence is introduced and several of their properties are established. Real life examples are taken for constructing counter examples and also for illustration. We have also discussed how these equalities can be applied in approximate reasoning and our latest proposal is no exception.