Organizational decisions and situation assessment are often made in groups, and decision and assessment processes involve various uncertain factors. To increase efficiently group decision-making, this study presents a new rational–political model as a systematic means of supporting group decision-making in an uncertain environment. The model takes advantage of both rational and political models and can handle inconsistent assessment, incomplete information and inaccurate opinions in deriving the best solution for the group decision under a sequential framework. The model particularly identifies three uncertain factors involved in a group decision-making process: decision makers’ roles, preferences for alternatives, and judgments for assessment-criteria. Based on this model, an intelligent multi-criteria fuzzy group decision-making method is proposed to deal with the three uncertain factors described by linguistic terms. The proposed method uses general fuzzy numbers and aggregates these factors into a group satisfactory decision that is in a most acceptable degree of the group. Inference rules are particularly introduced into the method for checking the consistence of individual preferences. Finally, a real case-study on a business situation assessment is illustrated by the proposed method.