New topological approach of rough set generalizations

Abstract

In this paper, we introduce a generalization of rough set theory using topological structures generated by any binary general relation. The class of all after-composed sets and the class of all fore-composed sets defined here are used to generate two topological spaces. These topologies are used to approximate sets topologically. Lower and upper approximations are defined topologically and some of their properties are studied using these topologies. Also, membership, equality, inclusion relations and power set notions in the generalized approximation space are studied. Many differences are shown between notions of ordinary set theory and notions of rough set theory. These notions introduced in this work are good future work to knowledge discovery and data mining.

Keywords:

• topological spaces
• binary relations
• lower approximation
• upper approximation
• rough sets
• approximation spaces

2010 AMS Subject Classifications :

• 54F99
• 68P01