Abstract

The concept of crisp sets was extended to the new set which was introduced by Pawlak namely rough sets. Some of the reasons for such extension are to undertake modelling, reasoning and other computing like modelling imprecise data. Many extensions have been made in various directions in order to improve the modelling capacity of the general rough sets. Among the several extensions of rough sets multigranulation rough set model is one among that and found high level practical usage since it deals with multiple granules. Granules with more than one equivalence relation enrich the detail level in the defined equivalence relation. Several fundamental properties of these types of rough sets have been studied. Pawlak introduced the types of rough sets in as an interesting characterization of rough sets by employing the ideas of lower and upper approximations of rough sets. There are two different ways of characterizing rough sets. The accuracy coefficient and the topological characterization introduced through the notion of types. As referred by Pawlak himself, in general rough sets by knowing the accuracy of a set, it is still difficult to tell exactly its topological structure and also the present knowledge about the topological structure of the set gives no information about its accuracy. Therefore in practical applications of rough sets it is better to combine both kinds of information about the borderline region, that is of the accuracy measure as well as the information about the topological classification of the set under consideration. Keeping this in mind, Tripathy and Mitra [9] have studied the types of rough sets by finding out the types of union and intersection of rough sets of different types. Later Raghavan et al have extended these results to the multigranular context in [12]. The database based validation of union of two multigranular rough sets was carried out by Raghavan in [16]. In this paper I provided other basic set operations of internal structure of multigranulation rough sets supported with database based validation.