A Comparative Analysis of Multigranular Approaches and on Topoligical Properties of Incomplete Pessimistic Multigranular Rough Fuzzy Sets
Bala Krushna Tripathy, M. Nagaraju · International Journal of Intelligent Systems and Applications · 2012
Rough sets, introduced by Pawlak as a model to capture imp reciseness in data have been a very useful tool in several applications.These basic rough sets are defined by taking equivalence relations over a universe.In order to enhance the modeling powers of rough sets, several extensions to the basic definit ion has been introduced over the past few years.Extending the single granular structure of research in classical rough set theory two notions of Multigranular approaches; Optimistic Multigranulat ion and Pessimistic Multigranulation have been introduced so far.Topological properties of rough sets along with accuracy measures are two important features of rough sets fro m the applicat ion point of view.Topological properties of Optimistic Mult igranular rough sets Optimistic Multigranular rough fuzzy sets and Pessimistic Multigranular rough sets have been studied.Incomplete information systems take care of missing values for items in data tables.Optimistic and pessimistic M GRS have also been extended to such type of inco mplete information systems.In this paper we provide a co mparat ive study of the two types of Multigranular approaches along with other related notions.Also, we extend the study to topological properties of inco mplete pessimistic M GRFS.These results hold both for co mplete and inco mplete information systems.