In traditional approaches to group decision making under risk (GDMR), there exists a problem that the hypothesis
is too ideal to perform feasibly, probably resulting in poor scientificalness and satisfaction of decision making as well as
low efficiency of decision procedure. To overcome above drawbacks, a selecting model and its distinguishing theorem are
presented to absorb multiple styles of fuzzy information and derive efficient prospects based on the prospect theory. After
that, an interactive approach to GDMR which is proved to be convergent is proposed by integrating with interactive learning
for outcome values. Numerical simulation cases show that the proposed approach not only ensures decision results to be
scientific and satisfactory by reflecting group members’ risk preferences, but also ensures decision procedure to be efficient
and feasible by balancing the relationship between information perfection levels and its acquisition costs.