Summary: In the face of increasing global competition and complexity of the socioeconomic environment, many organizations employ groups in decision making. Inexact or vague preferences have been discussed in the decision-making literature with a view to relaxing the burden of preference specifications imposed on the decision makers and thus taking into account the vagueness of human judgment. In this article, we present a multiperson decision-making method using fuzzy logic with a linguistic quantifier when each group member specifies incomplete judgment possibly both in terms of the evaluation of the performance of different alternatives with respect to multiple criteria and on the criteria themselves. Allowing for incomplete judgment in the model, however, makes a clear selection of the best alternative by the group more difficult. So, further interactions with the decision makers may proceed to the extent to compensate for the initial comfort of preference specifications. These interactions, however, may not guarantee the selection of the best alternative to implement. To circumvent this deadlock situation, we present a procedure for obtaining a satisfactory solution by the use of a linguistic-quantifier-guided aggregation that implies the fuzzy majority. This is an approach that combines a prescriptive decision method via mathematical programming and a well-established approximate solution method to aggregate multiple objects.