Covering Based Pessimistic Multigranular Rough Equalities and their Properties

Abstract

Abstract-The basic rough set theory introduced by Pawlak as a model to capture imprecision in data has been extended in many directions and covering based rough set models are among them. Again from the granular computing point of view, the basic rough sets are unigranular by nature. Two types of extensions to the context of multigranular computing are done; called the optimistic and pessimistic multigranulation by Qian et al in 2006 and 2010 respectively. Combining these two concepts of covering and multigranulation, covering based multigranular models have been introduced by Liu et al in 2012. Extending the stringent concept of mathematical equality of sets rough equalities were introduced by Novotny and Pawlak in 1985. Three more types of such approximate equalities were introduced by Tripathy in 2011. In this paper we study the approximate equalities introduced by Novotny and Pawlak from the pessimistic multigranular computing point of view and establish several of their properties. These concepts and properties are shown to be useful in approximate reasoning.

Covering Based Optimistic Multigranular Approximate Rough Equalities and their Properties

“…However, these notions of approximate equalities of sets boil down to equality of sets again. Recently the extension of these approximate equalities to the context of covering based rough sets for the pessimistic case is handled by Tripathy et al [21].…”

“…Fro m the point of view of granular computing, basic rough set theory deals with a single granulation [21]. However, in some application areas we need to handle more than one granulation at a time and this necessitated the development of mult i-granular rough sets (M GRS) [7], where at least two equivalence relations are taken for granulation of a universe.…”