Rough operations on Boolean algebras

In this paper, we introduce two pairs of rough operations on Boolean algebras. First we define a pair of rough approximations based on a partition of the unity of a Boolean algebra. We then propose a pair of generalized rough approximations on Boolean algebras after defining a basic assignment function between two different Boolean algebras. Finally, some discussions on the relationship between rough operations and some uncertainty measures are given to provide a better understanding of both rough operations and uncertainty measures on Boolean algebras.