الفهرس 
Granular ComputingOnly 14 pages are availabe for public view
 |  | from | 16 |  |  |
| | | from | 16 | | |
Abstract
In the present Thesis, we have introduced several different generalizations to “Rough Set Theory” in different directions:
(1) The first one is: General topological structure based on binary relations to define eight different approximations, which are dual
operators. These operators satisfied the all properties of the classical rough set theory that was introduced by Pawlak [52], without adding any conditions or restrictions.
Accordingly, we have introduced generalized definition to many different rough membership relations and functions, which are defined to be an easy tool to classify the sets and help for measuring exactness and roughness of sets. The existence of near
rough membership functions made us introduced the concept of near fuzzy sets as a new connection between important three theories “Rough Set Theory, Fuzzy Set Theory and General
Topology” which is very useful in application. Also, we generalized near rough sets in the frameworks of topological spaces.