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Abstract 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 (, q) (∈, ∈ ∨ q) -fuzzy ideals (semiprime and prime ideals) of ternary semirings are (, q) (∈, ∈ ∨ q) -fuzzy ideals (semiprime and prime ideals) respectively.
Bashir et al. (Wed,) studied this question.