Pawlak Approximations in the Framework of Nominal Sets
Andrei Alexandru and Gabriel Ciobanu
According to the axioms of the Fraenkel-Mostowski set theory, we define and study the lower and upper approximations of the (infinite) finitely supported subsets of some infinite nominal sets. We first translate the algebraic structures of lattices and the Galois connections into the Fraenkel-Mostowski framework, and then present their properties in terms of finitely supported objects. Nominal rough set approximations are expressed in terms of nominal Galois connections. Finally, by using new nominal fixed point theorems for nominal complete lattices and nominal Galois connections, we prove that the set of all definable finitely supported subsets of a nominal set form a nominal complete Boolean lattice.