Generalized roughness of three dimensional ($$\in ,\in \vee q$$)-fuzzy ideals in terms of set-valued homomorphism-Reference-Cited by-同舟云学术

Generalized roughness of three dimensional ($$\in ,\in \vee q$$)-fuzzy ideals in terms of set-valued homomorphism

Published:2024-05-29 Issue:1 Volume:14 Page:
ISSN:2045-2322
Container-title:Scientific Reports
language:en
Short-container-title:Sci Rep

Author:

Bashir Shahida,Mazhar Rabia,Kausar Nasreen,Yaman Saziye^ORCID,Ali Syed Suleman,Afzal Muneeb Ul Hassan

Abstract

AbstractThe 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.

Publisher

Springer Science and Business Media LLC

Link

https://www.nature.com/articles/s41598-024-62207-8.pdf

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