We introduce a notion of a probabilistic convergence transformation group, and present various natural examples including quotient probabilistic convergence transformation group. In doing so, we construct a probabilistic convergence structure on the group of homeomorphisms and look into a probabilistic convergence group that arises from probabilistic uniform convergence structure on function spaces. Given a probabilistic convergence space, and an arbitrary group, we construct a probabilistic convergence transformation group.

We identify two categories of quantale-valued convergence tower
spaces that are isomorphic to the categories of quantale-valued metric spaces
and quantale-valued partial metric spaces, respectively. As an application we
state a quantale-valued metrization theorem for quantale-valued convergence
tower groups

Considering a complete Heyting algebra $\mathbb{H}$, we introduce a notion of stratified $\mathbb{H}$-convergence semigroup. We develop some basic facts on the subject, besides obtaining conditions under which a stratified $\mathbb{H}$-convergence semigroup is a stratified $\mathbb{H}$-convergence group. We supply a variety of natural examples; and show that every stratified $\mathbb{H}$-convergence semigroup with identity is a stratified $\mathbb{H}$-quasi-uniform convergence space.

J48. Alkhomsan, M. N., Hossain, M. A., Rahman, S. M. M., & Masud, M. (2017). Situation Awareness in Ambient Assisted Living for Smart Healthcare. IEEE Access, 5(1)