The necessary and sufficient conditions for bimigrativity of uninorms over overlap functions

Building on the work of Lopez-Molina et al. [27], in this paper, we investigate the bimigrativity of uninorms over any fixed overlap function. First, we introduce the concept of $(\alpha ,\beta )$-bimigrative uninorms with respect to a given overlap function O. Moreover, we provide detailed equivalent characterizations and related properties of the $(\alpha ,\beta )$-bimigrativity equation for uninorms U that belong to different classes, including $U\min$, $U\max$, idempotent uninorms, representable uninorms, and continuous uninorms on ${(0,1)}^2$.