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

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Bashir S., Mazhar R., KAUSAR N., Yaman S., Ali S. S., Afzal M. U. H.

Scientific Reports, vol.14, no.1, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.1038/s41598-024-62207-8
  • Journal Name: Scientific Reports
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, BIOSIS, Chemical Abstracts Core, MEDLINE, Veterinary Science Database, Directory of Open Access Journals
  • Keywords: (∈,∈∨q)-fuzzy ideal, Lower and upper approximations, Set-valued homomorphism, Strong set-valued homomorphism, Ternary semiring
  • Yıldız Technical University Affiliated: Yes


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.