A Novel Study of Fuzzy Bi-Ideals in Ordered Semirings
Ghulam Muhiuddin, Nabilah Abughazalah, Ahsan Mahboob, Deena Al-Kadi- Geometry and Topology
- Logic
- Mathematical Physics
- Algebra and Number Theory
- Analysis
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.