T-rough Semiprime Ideals on Commutative Rings


S. B. Hosseini - Department of Mathematics, Islamic Azad University, Sari Branch, Sari, Iran.


Rough sets were originally proposed in the presence of an equivalence relation. An equivalence relation is sometimes difficult to be obtained in rearward problems due to the vagueness and incompleteness of human knowledge. The purpose of this paper is to introduce and discuss the concept of T-rough semiprime ideal, T-rough fuzzy semiprime ideal and T-rough quotient ideal in a commutative ring which are a generalization of rough set and approximation theory. We compare relation between a rough ideal and a T-rough ideal and prove some theorems.