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Recently, fuzzy multisets have come to the forefront of scientists’ interest and have been used for algebraic structures such as groups, rings, and near rings. In this paper, we first summarize the knowledge about algebraic structure of fuzzy multisets such as fuzzy multi-subnear rings and fuzzy multi-ideals of near rings. Then we recall the results from our related previous work, where we defined different operations on fuzzy multi-ideals of near rings and we generalized some known results for fuzzy ideals of near rings to fuzzy multi-ideals of near rings. Finally, we define anti-fuzzy multi-subnear rings (multi-ideals) of near rings and study their properties.

Anti-Fuzzy Multi-Ideals of Near Ring