Abstract Recently, as an addendum to Qiao and Hu (2018) [21] , Zhu and Hu (2020) [25] studied the α-migrativity of overlap and grouping functions over uninorms and nullnorms. Later on, Zhou and Yan (2019) [24] further investigated the α-migrativity properties of overlap functions over uninorms. They showed equivalent characterizations of the ( α , U ) -migrativity equation when the uninorm U belongs to one certain class (e.g., U min , U max , the family of idempotent uninorms, representable uninorms or uninorms continuous on ] 0 , 1 [ 2 ). However, we find that Propositions 3.5, 3.8 and Remark 3.5 (2) presented by Zhu and Hu (2020) [25] are incorrect. In this note, at first, we establish the updated results. And then, we study the α-migrativity of overlap functions over t-norms when t-norms are continuous and give their characterizations. In particular, we point out that the relationship between the α-migrativity of overlap functions over uninorms and the α-migrativity of uninorms over overlap functions. Finally, we discuss the ( α , U ) -migrativity equation for grouping functions using an analogous method.

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关于单范式上重叠函数的迁移特性的简短说明

摘要 最近，作为乔和胡 (2018) [21] 的附录，朱和胡 (2020) [25] 研究了重叠和分组函数在单范式和零范式上的 α-迁移性。随后，Zhou and Yan (2019) [24] 进一步研究了重叠函数在单项上的 α-迁移特性。当单范式 U 属于某一类（例如，U min , U max ，幂等单项式家族，可表示单项式或在 ] 0 , 1 [ 2 上连续的单项式）。但是，我们发现 Zhu 和 Hu (2020) [25] 提出的命题 3.5、3.8 和备注 3.5 (2) 是不正确的。在本笔记中，我们首先建立更新的结果。然后，我们研究了当 t 范数连续时重叠函数在 t 范数上的 α 迁移性并给出了它们的特征。特别地，我们指出重叠函数在单项上的α-迁移率与单项在重叠函数上的α-迁移率之间的关系。最后，我们讨论了使用类似方法对函数进行分组的 (α, U) - 迁移方程。