On Some Topological Properties of Pessimistic Multigranular Rough Sets
Bala Krushna Tripathy, M. Nagaraju · International Journal of Intelligent Systems and Applications · 2012
Rough set theory was introduced by Pawlak as a model to capture imp reciseness in data and since then it has been established to be a very efficient tool for this purpose.The definition of basic rough sets depends upon a single equivalence relation defined on the universe or several equivalence relations taken one each at a time.There have been several extensions to the basic rough sets introduced since then in the literature.Fro m the granular computing point of view, research in classical rough set theory is done by taking a single granulation.It has been extended to mu ltigranular rough set (MGRS) model, where the set approximations are defined by taking mu ltip le equivalence relat ions on the universe simultaneously.Multigranular rough sets are of two types; namely optimistic M GRS and pessimistic M GRS.Topological properties of rough sets introduced by Pawlak in terms of their types were studied by Tripathy and Mitra to find the types of the union, intersection and complement of such sets.Tripathy and Raghavan have extended the topological properties of basic single granular rough sets to the optimistic M GRS context.Inco mplete informat ion systems take care of missing values for items in data tables.MGRS has also been extended to such type of incomplete information systems.In this paper we have carried out the study of topological properties of pessimistic M GRS by finding out the types of the union, intersection and complement of such sets.Also, we have provided proofs and examples to illustrate that the multip le entries in the table can actually occur in practice.Our results hold for both complete and incomp lete information systems.The mu ltip le entries in the tables occur due to imp reciseness and ambiguity in the informat ion.This is very common in many of the real life situations and needed to be addressed to handle such situations in efficient manner.