In this study, two main goals were achieved. In near-ring N, we have proven that, the level set is a subnear-ring of N if and only if the fuzzy set is the fuzzy subnear-ring of N. Similarly, in hyper near-ring R, it has been proven that, a fuzzy set is a fuzzy hypernear-ring if and only if level set is a sub-hypernear-ring of R. A direct proof method was used to reach these results, which will contribute to expanding the field of study on fuzzy near-ring and fuzzy hyper near-rings.
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Yasser AbouElwan (2024) studied this question.
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