Generalized roughness of three dimensional ( $\in ,\in \vee q$ )-fuzzy ideals in terms of set-valued homomorphism

The objective of this study is to generalize the roughness of a fuzzy set-in three-dimensional structure by introducing ternary multiplication. Many results and theorems of rough fuzzy ideals have been extended from semigroup and semiring, to ternary semiring by introducing the definition of a rough fuzzy subset of ternary semiring. By using the concept of set-valued homomorphism and strong set-valued homomorphism, it is proved generalized lower and upper approximations of $(\in ,\in \vee q)$ -fuzzy ideals (semiprime and prime ideals) of ternary semirings are $(\in ,\in \vee q)$ -fuzzy ideals (semiprime and prime ideals) respectively.