  This work introduces a new abstraction technique for reducing the state space
of large, discrete-time labelled Markov chains. The abstraction leverages the
semantics of interval Markov decision processes and the existing notion of
approximate probabilistic bisimulation. Whilst standard abstractions make use
of abstract points that are taken from the state space of the concrete model
and which serve as representatives for sets of concrete states, in this work
the abstract structure is constructed considering abstract points that are not
necessarily selected from the states of the concrete model, rather they are a
function of these states. The resulting model presents a smaller one-step
bisimulation error, when compared to a like-sized, standard Markov chain
abstraction. We outline a method to perform probabilistic model checking, and
show that the computational complexity of the new method is comparable to that
of standard abstractions based on approximate probabilistic bisimulations.
