*3.1. Research Development*

Figure 1 illustrates the selection process, which is sequentially presented in three steps. In the first step, the decision-maker examines the material, interviews the experts, and surveys managers to determine the criteria and sub-criteria affecting to decision making. In the second step data are then processed using the FANP method to rank the criteria. Results from the FANP method are used for the input and output of the DEA model. The DEA model is implemented in the final stage.

**Figure 1.** Research process.

#### **Step 1**: *Determining evaluation criteria and sub-criteria*

Determine the key criteria and sub-criteria for a comprehensive assessment of the potential supplier. At this stage, the identification of key criteria and sub-criteria is based on a review of the literature and scientific reports related to the content of the research to determine the necessary criteria for the topic [50]. After identifying the groups of criteria required, the decision-maker should select the potential supplier that matches the set criteria. Here, the criteria are defined as four main criteria and 15 sub-criteria, as shown in Figure 2.

#### **Step 2**: *Implementing the FANP technique*

Incorporating hybrid fuzzy set theory into the ANP model is the most effective tool for addressing complex problems of decision-making, which has a connection with various qualitative criteria [37]. As can be seen from the solution algorithm in this technique, as presented in Figure 3, at first, the decision-making hierarchical structure is determined to assist the selection [71].

#### **Step 3**: *Implementation of the DEA model*

In this study, the FANP and DEA techniques for efficiency measurement have advantages over other fuzzy ANP approaches. In this step, several DEA models, including the Charnes–Cooper–Rhodes model (CCR model), Banker–Charnes–Cooper model (BCC model), Slacks-Based Measure model (SBM model), and Super Slacks-Based Measure model (Super SBM model) are applied to rank suppliers and potential suppliers.

**Figure 2.** A triangular fuzzy number (TFN).

**Figure 3.** Triangular fuzzy number (TFN).
