T-rough Ideal and T-rough Fuzzy Ideal in a Semigroup

T-rough sets was introduced in [4]. Our aim in this paper is to introduce the concept of T-rough ideal , T-rough quotient ideal and T-rough fuzzy ideal and study on a set-valued homomorphism for semigroups. 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. From this point of view, in this paper, we generalized some theorems that they are proved in [21].

Keywords:

Rough set , rough ideal , rough prime ideal , T-rough set , set- valued homomorphism , T-rough ideal , T-rough fuzzy ideal