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Generalized roughness of three dimensional ( )-fuzzy ideals in terms of set-valued homomorphism
Shahida Bashir1, Rabia Mazhar1, Nasreen Kausar2
1Department of Mathematics, University of Gujrat, Gujrat, 50700, Pakistan.
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 -fuzzy ideals (semiprime and prime ideals) of ternary semirings are -fuzzy ideals (semiprime and prime ideals) respectively.
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