A fuzzy multiple objective decision making approach is proposed. This approach is based on the desirable features of compromise programming and the fuzzy set theory. The proposed two-phase approach guarantees both nondominated and balanced solutions for both the crisp and the fuzzy multiple objective decision making problems. It is shown that compromise programming and fuzzy set approach for multiple objective decision making are essentially equivalent under certain conditions. Furthermore, it is shown that compromise programming does not guarantee nondominated solutions when the distance parameter is assumed the value of infinity and the solution of the resulting programming problem is not unique. The most important aspect in the fuzzy approach is the compensatory or non-compensatory nature of the aggregate operator. It is shown that a nondominated solution can always be obtained in phase two, regardless of the uniqueness of the solution. This two-phase approach is applied to solve the fuzzy multiple objective decision making problems with both fuzzy constraints and fuzzy parameters.