Types Of Rough Sets Research Articles

New types of rough Pythagorean fuzzy UP-filters of UP-algebras

The aim of this paper is to introduce nine types of rough Pythagorean fuzzy sets in UP-algebras and nine types of rough sets in UP-algebras. Then we study relation of these rough Pythagorean fuzzy sets and new types of Pythagorean fuzzy UP-filter under equivalence (congruence) relation. Moreover, we will also discuss \(t\)-level subsets of rough Pythagorean fuzzy sets in UP-algebras to study the relationships between rough Pythagorean fuzzy sets and rough sets in UP-algebras which we defined them above. Finally, we discuss the concept of homomorphisms between IUP-algebras and also study the direct and inverse images of four special subsets.

Topological properties of multigranular rough sets on intuitionistic fuzzy approximation spaces

Two of the extensions of the basic rough set model introduced by Pawlak in 1982 is the rough sets on fuzzy approximation spaces introduced by De et al. in 2003 and its extension rough sets on intuitionistic fuzzy approximation spaces in 2006 by Tripathy. The model of Tripathy is dependent upon an intuitionistic fuzzy proximity relation. In an attempt to handle multiple granulations simultaneously two types of multigranulations called the optimistic and pessimistic multigranulation were introduced by Qian et al. in 2006 and 2010 respectively. The notion of multigranular rough sets over intuitionistic fuzzy approximation spaces were introduced by Tripathy et al. in 2018. Topological properties of rough sets, introduced by Pawlak have been studied extensively for different types of rough sets by Tripathy et al. Continuing this, here we introduce and study the concept of topological properties of multigranular rough sets on intuitionistic fuzzy approximation spaces.

Topological properties of multigranular rough sets on intuitionistic fuzzy approximation spaces

Two of the extensions of the basic rough set model introduced by Pawlak in 1982 is the rough sets on fuzzy approximation spaces introduced by De et al. in 2003 and its extension rough sets on intuitionistic fuzzy approximation spaces in 2006 by Tripathy. The model of Tripathy is dependent upon an intuitionistic fuzzy proximity relation. In an attempt to handle multiple granulations simultaneously two types of multigranulations called the optimistic and pessimistic multigranulation were introduced by Qian et al. in 2006 and 2010 respectively. The notion of multigranular rough sets over intuitionistic fuzzy approximation spaces were introduced by Tripathy et al. in 2018. Topological properties of rough sets, introduced by Pawlak have been studied extensively for different types of rough sets by Tripathy et al. Continuing this, here we introduce and study the concept of topological properties of multigranular rough sets on intuitionistic fuzzy approximation spaces.

Relationships between generalized rough sets based on covering and reflexive neighborhood system

Rough set theory is an important tool to deal with uncertainty, granularity and incompleteness of knowledge. The covering-based rough sets is one of the most important extensions of the classical Pawlak rough sets. In covering-based rough set theory, many types of rough sets were already defined in the literature. To find out the relationships among different types of covering-based rough sets and give an axiomatic definition is a very important issue. The generalized rough sets in neighborhood system is another important extension of the classical Pawlak rough sets. In this paper, we investigate relationships between covering-based rough sets and generalized rough sets in neighborhood system. Then, twenty-three types of the element based, the granule based and the subsystem based definitions of covering approximation operators are unified under the framework of generalized approximation operators in neighborhood systems. Moreover, properties of the generalized approximation operators in neighborhood systems are presented.

Rough sets on fuzzy approximation spaces and applications to distributed knowledge systems

A fuzzy relation is an extension of crisp relation on any set U. Fuzzy proximity relations on U are much more general and abundant than equivalence relations. The fuzzy approximation space which depends upon a fuzzy proximity relation defined on a set U is a generalisation of the concept of knowledge base. So, rough sets defined on fuzzy approximation spaces extend the concept of rough sets on knowledge bases. The results of the present paper extend the basic properties of rough sets and results involving set theoretic operations on types of rough sets that have been established in Tripathy and Mitra (2008).