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Sci Rep
; 14(1): 12301, 2024 May 29.
Article
in English
| MEDLINE
| ID: mdl-38811631
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 ) -fuzzy ideals (semiprime and prime ideals) of ternary semirings are ( ∈ , ∈ ⨠q ) -fuzzy ideals (semiprime and prime ideals) respectively.