The ability of the analytical hierarchy process (AHP) when applied to the choice problem in the context of group decision making under uncertainty has been often criticised. AHP is not able to fully capture the various opinions and the uncertainty associated with the lack of information. This work develops an integrated constrained fuzzy stochastic analytic hierarchy process (IC-FSAHP) method in order to deal with the aforementioned drawbacks. IC-FSAHP combines two existing fuzzy AHP (FAHP) methods and further extends its applicability by implementing stochastic simulations. A case study has been conducted in order to assess the ability of IC-FSAHP; the results showed that IC-FSAHP is able to capture the uncertainty and multiple DMs' opinions. This paper also discusses the effect that the number of DMs has in enhancing rank discrimination. Besides, the possibility of the occurrence of rank reversal because of the use of IC-FSAHP has been analysed. The results showed that the ranking of alternatives was preserved throughout the changes in the number of alternatives, however, rank reversal occurred in the case of changes in judgements scales. By comparing the U-uncertainty in fuzzy global priorities obtained using IC-FSAHP to that obtained using an existing FSAHP method, we show that our method is capable of minimising the risk of losing important knowledge during the computations. We also discuss how IC-FSAHP can decrease the uncertainty and increase the reliability of the decisions by means of robust computations.