A Comparative Analysis of Multigranular Approaches and on Topoligical Properties of Incomplete Pessimistic Multigranular Rough Fuzzy Sets

Abstract

Rough sets, introduced by Pawlak as a model to capture impreciseness 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 definition 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 Multigranulation and Pessimistic Multigranulation have been introduced so far. Topological properties of rough sets along with accuracy measures are two important features of rough sets from the application point of view. Topological properties of Optimistic Multigranular 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 MGRS have also been extended to such type of incomplete information systems. In this paper we provide a comparative study of the two types of Multigranular approaches along with other related notions. Also, we extend the study to topological properties of incomplete pessimistic MGRFS. These results hold both for complete and incomplete information systems.