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

Abstract

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 $$(\in , \in \vee q)$$ ( ∈ , ∈ ∨ q ) -fuzzy ideals (semiprime and prime ideals) of ternary semirings are $$(\in ,\in \vee q)$$ ( ∈ , ∈ ∨ q ) -fuzzy ideals (semiprime and prime ideals) respectively.

Keywords

• Ternary semiring
• $$(\in ,\in \vee q)$$ ( ∈ , ∈ ∨ q ) -fuzzy ideal
• Lower and upper approximations
• Set-valued homomorphism
• Strong set-valued homomorphism