An extended 2-tuple linguistic DEA for solving MAGDM problems considering the influence relationships among attributes

- MAGDM problems with unknown DM weights and attribute weights are researched.
- The dynamic DM weights vary from different attributes and different alternatives.
- The 2-tuple linguistic DEA is proposed.
- DEMATEL combines with DEA to analyze the influence relationships among attributes.
- Alternatives are evaluated using the influential weights and the weights from DEA.

The main purpose of this paper is to propose an extended data envelopment analysis (DEA) approach for solving multiple attribute group decision making (MAGDM) problems with unknown decision maker (DM) weights and attribute weights. The 2-tuple linguistic representation model is more suitable to deal with linguistic evaluations than the extension principle and the symbolic method. So we propose a 2-tuple linguistic DEA model and objective DM weights determination method in 2-tuple MAGDM problems. The DMs' objective weights are dynamic with respect to each attribute over different alternatives, which are determined according to the grey relational degree of the decision information DM given with the ideal decision information obtained by solving a weighted least square optimization model. The optimized attribute weights based on the DEA model only reflect the beneficial side to each alternative and ignore the objective side like influence relationships among attributes. Therefore, a 2-tuple linguistic DEMATEL technique is presented and applied to adjust the attribute weights obtained by DEA, and then the comprehensive attribute weights are derived. Finally, the evaluation values of alternatives are obtained based on the comprehensive attribute weights according to the efficiency evaluation method of DEA. A case study is put forward to validate the effectiveness of the proposed approach.