Date Received: 22-07-2016 / Date Accepted: 26-08-2016
Fuzzy set theory and rough set theory have many applications in the fields of data mining, knowledge representation. Nowadays, there are many extensions which are mentioned along with the properties and applications of them. Concept T-rough set which allows us to discover knowledge is expressed as a map. In this paper, we introduce the concept of T-rough fuzzy set on crisp approximation spaces; their properties and fuzzy topology spaces which based on definable sets are studied. Then, by the same way, we also introduced the concept of collective T - rough fuzzy fuzzy approximation space, it is seen as a more general concept ofT-rough fuzzy set on crisp approximation spaces.
