Generalized roughness of three dimensional ( $$\in ,\in \vee q$$ ∈ , ∈ ∨ q )-fuzzy ideals in terms of set-valued homomorphism
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 o...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2024-05-01
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| Series: | Scientific Reports |
| Subjects: | |
| Online Access: | https://doi.org/10.1038/s41598-024-62207-8 |
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| Summary: | 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. |
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| ISSN: | 2045-2322 |