Evaluating and selecting alternatives from available alternatives with respect to multiple, often conflicting criteria in a group decision making setting is complex and challenging due to the risk associated with the uncertainty and imprecision existent in the human decision making process. To effectively solve this problem, this paper proposes a risk-oriented group decision making approach for adequately modelling the inherent risk in the multi-criteria group decision making process. Linguistic variables approximated by triangular fuzzy numbers are used for representing the subjective and imprecise assessments of the decision maker in evaluating the relative importance of the evaluation criteria and the performance of alternatives. The concept of ideal solutions is applied for calculating the overall performance index for each alternative across all criteria so that the complex and unreliable process of comparing fuzzy utilities is avoided. An example is presented to demonstrate the applicability of the proposed approach for solving the information system project selection problem in real world settings.