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On fuzzy sub-semi-rings of nexuses
AIMS Mathematics 2024, 9(12): 36140-36157
Published: 15 December 2024
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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:NM, we showed that if μFSUBS(N), then f(μ)FSUBS(M) and if μFSUBS(M) then fμFSUBS(N). Finally, we verified some concepts of fuzzy quotient of a nexus semi-ring.

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