@article{Nazemi Niya2024, 
author = {Vajiheh Nazemi Niya and Hojat Babaei and Akbar Rezaei},
title = {On fuzzy sub-semi-rings of nexuses},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {12},
pages = {36140-36157},
keywords = {nexus, semi-ring, fuzzy sub-semi-ring, semi-ring homomorphism, fuzzy quotient},
url = {https://www.sciopen.com/article/10.3934/math.20241715},
doi = {10.3934/math.20241715},
abstract = {In this paper, we first constructed a semi-ring on a nexus and then defined a fuzzy sub-semi-ring associated with a nexus  N. We investigated some properties and applications. Fuzzy versions of some well-known crisp concepts are provided over a nexus. We verified some applications of this fuzzy on semi-ring  N. We obtained some relationships between sub-semi-ring and fuzzy sub-semi-ring of  N. However, these relationships were not true for ideals. We put a condition on fuzzy sub-semi-ring so that these relationships were true for ideals. We defined strong fuzzy sub-semi-ring on  N. For strong fuzzy sub-semi-ring on  N and for every  α∈[0,μ(0)], the level set  μα was an ideal of  N. For some strong fuzzy sub-semi-rings  μ, we verified when  μα was a prime ideal of  N. In the following, for a semi-ring homomorphism  f:N⟶M, we showed that if  μ∈FSUBS(N), then  f(μ)∈FSUBS(M) and if  μ∈FSUBS(M) then  f∘μ∈FSUBS(N). Finally, we verified some concepts of fuzzy quotient of a nexus semi-ring.}
}