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Keywords = intra-regular ordered semirings

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13 pages, 314 KB  
Article
A Novel Study of Fuzzy Bi-Ideals in Ordered Semirings
by Ghulam Muhiuddin, Nabilah Abughazalah, Ahsan Mahboob and Deena Al-Kadi
Axioms 2023, 12(7), 626; https://doi.org/10.3390/axioms12070626 - 24 Jun 2023
Cited by 3 | Viewed by 1486
Abstract
In this study, by generalizing the notion of fuzzy bi-ideals of ordered semirings, the notion of (,(κ*,qκ))-fuzzy bi-ideals is established. We prove that [...] Read more.
In this study, by generalizing the notion of fuzzy bi-ideals of ordered semirings, the notion of (,(κ*,qκ))-fuzzy bi-ideals is established. We prove that (,(κ*,qκ))-fuzzy bi-ideals are fuzzy bi-ideals but that the converse is not true, and an example is provided to support this proof. A condition is given under which fuzzy bi-ideals of ordered semirings coincide with (,(κ*,qκ))-fuzzy bi-ideals. An equivalent condition and certain correspondences between bi-ideals and (,(κ*,qκ))-fuzzy bi-ideals are presented. Moreover, the (κ*,κ)-lower part of (,(κ*,qκ))-fuzzy bi-ideals is described and depicted in terms of several classes of ordered semirings. Furthermore, it is shown that the ordered semiring is bi-simple if and only if it is (,(κ*,qκ))-fuzzy bi-simple. Full article
(This article belongs to the Special Issue Recent Advances in Fuzzy Sets and Related Topics)
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