## 3 Application  
In this section, four AM machine selection examples are introduced to illustrate the application of the proposed approach. Example 1 [12]: DMD (Direct Metal Deposition), DMLS (Direct Metal Laser Sintering), EBM (Electron Beam Melting), LENS (Laser Engineered Net Shaping), SLM (Selective Laser Melting), and SLS (Selective Laser Sintering) are six AM processes. One AM machine is selected under each AM process, which makes up six alternative AM machines. This article still uses each AM process to represent its corresponding AM machine. The attributes used to select these AM machines are ultimate tensile strength (MPa), Rockwell hardness (HRC), density (%), detail capability (mm), geometric complexity (numu), build time (hrs), and part cost ($). Table 6 lists the alternative AM machines and the attributes considered for each alternative. The weights of the seven attributes are 0.167, 0.144, 0.071, 0.024, 0.214, 0.190, and 0.190. Example 2 [10]: SLA3500, SLS2500, FDM8000, LOM1015, Quadra, and Z402 are six alternative AM machines. The attributes used to select these AM machines are dimensional accuracy (\(\mu\)m), surface roughness (\(\mu\)m), tensile strength (MPa), elongation (\(\%\)), part cost, and build time. Table 7 lists the alternative AM machines and the attributes considered for each alternative. The weights of the six attributes are 0.1113, 0.1113, 0.0634, 0.0634, 0.3253, and 0.3253. Example 3[28]: 3D Systems Viper & Protogen 18420, 3D Systems Viper & Somos Next, M3 Linear & CL 20-316L, EOSCINT & PA 2200, EOSCINT & PA 3200 GF, and APCAMA2 & Ti6A/4v ELI are six alternative AM machines. The attributes used to select these AM machines are cost (\(\mathfrak{C}\)), roughness (\(\mu\)m), build time (hrs), strength (MPa), and density (g/cm\({}^{3}\)). Table 8 lists the alternative AM machines and the attributes considered for each alternative. The weights of the five attributes are 0.15, 0.15,  
Using the proposed approach, the AM machine selection problems in the above four examples can be solved. As an example, the AM machine selection problem in Example 1 is solved via the eight specific steps of the proposed approach. The intermediate and final results are as follows:  
A total of 36 object property assertions are created. By executing the attribute values with the automatic generation program, the DL ontology will automatically generate 36 data property assertions. The results are shown in Figure 3.  
Figure 3: _Cont._  
A decision matrix \(M\) is established as:  
\[M= \begin{bmatrix}1800&53&100&1.016&6&25.44&77.78\\ 600&21&95&0.3&10&41.47&1150.18\\ 1430&50&100&1.2&10&10.41&315.03\\ 1703&53&100&0.762&6&5.03&145.51\\ 2000&60&99.5&0.15&10&27.45&679.15\\ 606&15&100&0.6&10&41.47&453.27\\ \end{bmatrix} \]  
A fuzzy decision matrix \(M^{{}^{\prime}}\) is established as:  
\[M^{{}^{\prime}}= \begin{bmatrix}\langle 0.5009\rangle&\langle 0.4763\rangle& \langle 0.5880\rangle&\langle 0.5411\rangle&\langle 0.2762\rangle&\langle 0.6393\rangle& \langle 0.9465\rangle\\ \langle 0.1670\rangle&\langle 0.1887\rangle&\langle 0.6086\rangle&\langle 0.1598 \rangle&\langle 0.4603\rangle&\langle 0.4120\rangle&\langle 0.2093\rangle\\ \langle 0.3980\rangle&\langle 0.4493\rangle&\langle 0.5880\rangle&\langle 0.6391\rangle& \langle 0.4603\rangle&\langle 0.8524\rangle&\langle 0.7834\rangle\\ \langle 0.4739\rangle&\langle 0.4763\rangle&\langle 0.5880\rangle&\langle 0.4058 \rangle&\langle 0.2762\rangle&\langle 0.9287\rangle&\langle 0.9000\rangle\\ \langle 0.5566\rangle&\langle 0.5392\rangle&\langle 0.5901\rangle&\langle 0.0799\rangle& \langle 0.4603\rangle&\langle 0.6108\rangle&\langle 0.5331\rangle\\ \end{bmatrix} \]  
The relative loss functions are shown in Table 10.  
Figure 3: Automatic generation of attribute values for Example 1. The comprehensive results are shown in Table 11.  
The comprehensive thresholds are shown in Table 12.  
9. Make the judgment of each alternative.