Generalized roughness of three dimensional ( ∈ , ∈ ∨ q)-fuzzy ideals in terms of set-valued homomorphism - Bashir, Shahida; Mazhar, Rabia; Kausar, Nasreen; Yaman, Saziye; Ali, Syed Suleman; Afzal, Muneeb Ul Hassan (NATURE PORTFOLIO, 2024)
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 ( is an element of , is an element of boolean OR q )-fuzzy ideals (semiprime and prime ideals) of ternary semirings are ( is an element of , is an element of boolean OR q )-fuzzy ideals (semiprime and prime ideals) respectively.
Keywords: Ternary semiring; ( is an element of , is an element of boolean OR q )-fuzzy ideal; Lower and upper approximations; Set-valued homomorphism; Strong set-valued homomorphism; Science & Technology - Other Topics