A multi-criteria synthesis strategy for heat-exchanger networks (HENs) simultaneously considering minimum utility consumption, maximum source-stream temperature flexibility, and even minimum number of matches is proposed. The flexible HEN synthesis problem is formulated as a multi-objective mixed-integer linear programming (MO-MILP). For handling the multiple conflict design targets, a two-phase fuzzy multi-criteria decision-making method is presented to attain a best compromised solution. Two numerical examples with flexibility preferences in source-stream temperatures are supplied, demonstrating that the proposed strategy can provide definite and feasible compensatory solutions for multi-criteria HEN synthesis problems. (C) 2004 Elsevier B.V. All fights reserved.