Selecting the most suitable mineral processing equipment among feasible alternatives with respect to multiple conflicting criteria is considered a Multiple Criteria Decision Making (MCDM) problem. For example, a type of crusher that might allow a very high throughput is less likely to be used in a mobile plant, so trade-offs between these type of criteria need to be clearly defined in the decision making process. One of the most frequently used MCDM methods is the Analytical Hierarchy Process (AHP) method, which relies on judgements from decision makers that allow for comparisons to be made between alternatives (e.g. the type of equipment) or criteria (e.g. the characteristics of the equipment that are of interest). However, AHP is not able to capture the uncertainty associated with the various decision makers’ judgements and the lack of precise information. An integrated constrained fuzzy stochastic analytic hierarchy process (IC-FSAHP) is a new hybrid MCDM method that can be used to overcome the aforementioned limitations of AHP. In order to understand the robustness of AHP based methods, a sensitivity analysis of the decision making results is required. However, sensitivity analyses are not often carried out for fuzzy AHP methods, arguably because of the complexity of some of the procedures involved, the computation time required and the limited resources available to do so. The main objective of this paper is therefore to propose a new sensitivity analysis approach by applying an additional fuzzification factor and disagreement level of decision makers in order to model uncertainty. For this purpose, a case study for the selection of primary crushers was considered. Five types of primary crushers were evaluated with respect to six criteria to showcase the applicability of the proposed approach to assess IC-FSAHP. The results obtained showcase that the proposed sensitivity analysis approach is capable of providing extensive and useful “what-if” information on the decision making results.