A TOPSIS, VIKOR and DEA integrated evaluation method with belief structure under uncertainty to rank alternatives

This study proposes a combined method, based on a new compromised solution method and DEA to evaluate the efficiency of DMUs. By using TOPSIS and VIKOR methods two concepts are considered simultaneously. First, the optimal alternative is closer to positive ideal solution and farther from negative ideal solution. Second, the proposed method provides a maximum 'group utility' for the 'majority' and a minimum of an individual regret for the 'opponent'. In this method, weight of efficiency obtained from new compromised solution method is multiplied by the weight of CCR model of DEA. The problem involves BELIEF parameters in the solution procedure. Thus, the new proposed method that applied the advantages of TOPSIS, VIKOR and DEA and BELIEF structure simultaneously was used as a group decision making problem to exploit many experts' judgments. Finally, to illustrate the proposed method, an illustrative example is provided.