On fuzzy sub-semi-rings of nexuses

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 $\alpha \in [0,\mu (0)]$, the level set ${\mu }^{\alpha }$ was an ideal of $N$. For some strong fuzzy sub-semi-rings $\mu$, we verified when ${\mu }^{\alpha }$ was a prime ideal of $N$. In the following, for a semi-ring homomorphism $f:N⟶M$, we showed that if $\mu \in FSU{B}_S(N)$, then $f(\mu )\in FSU{B}_S(M)$ and if $\mu \in FSU{B}_S(M)$ then $f\circ \mu \in FSU{B}_S(N)$. Finally, we verified some concepts of fuzzy quotient of a nexus semi-ring.