This paper presents interactive procedures for solving a multiple criteria group decision making (MCGDM) problem with incomplete information when multiple decision makers are involved. It is difficult for group members participating in the decision making process to articulate their preferences with cardinal values. Therefore, we represent their preferences with utility ranges obtained by solving linear programming (LP) problems with incompletely specified information, find conflicting judgments, if any in their specified information, and suggest interaction processes to help the group reach a consensus. This paper will provide an algorithmic basis for a normative and interactive knowledge based group decision support system. (C) 1998 Elsevier Science B.V. All rights reserved.