**5. Discussion and Comparison Analysis**

In order to confirm the obtained results, similar calculations were performed by applying the TOPSIS method with the Euclidean distance, and the two commonly used approaches in the case of applying neutrosophic sets (i.e., the score function and the cosine similarity measure).

The calculation details obtained by using the TOPSIS method and the Euclidean distance are presented in Table 9. As can be observed from Table 9, the application of the TOPSIS method with the Euclidean distance produced the same ranking results.

To check the stability of the obtained ranking order of the alternatives, the calculation was repeated five times with the weighting vectors shown in Table 10.


**Table 10.** The weighting vectors used for the recalculation.

The ranking results obtained by using the five different weighting vectors and the two distances are given in Tables 11 and 12.

**Table 11.** The ranking results obtained by using the Hamming distance and different *W<sup>i</sup>* .


**Table 12.** The ranking results obtained by using the Euclidean distance and different *W<sup>i</sup>* .


The use of different weighting vectors caused changes in the ranking order in two cases, namely: *W*<sup>2</sup> and *W*5. In the first case (*W*2), both distances gave the same ranking order, whereas in the second case (*W*5), there was a difference in the second- and third-ranked alternatives.

Based on the foregoing, it can be concluded that the developed extension of the TOPSIS method can be employed with any of the two previously considered distances (i.e., with the one easier to calculate such as the Hamming distance, or the one slightly more complex to calculate in the case of using SVNNs like Euclidean distance).

To finally verify the ranking results obtained by the developed adaptation of the TOPSIS method, an additional ranking of the strategies was performed by using two commonly used approaches (i.e., the score function and the cosine similarity measure). The values of the score function and the cosine similarity measure for the considered alternatives were determined by applying Equations (6) and (7), respectively, to the overall ratings calculated by applying Equation (8). In this calculation, all the criteria again had the same importance of *w<sup>j</sup>* = 0.20. The achieved ranking results are shown in Table 13.

**Table 13.** The ranking by using the score function and the cosine similarity measure.


Table 13 allows us to note that the obtained results were partly different from the results shown in Tables 8 and 9. The difference occurs with the alternative ECDS3, which now shared first place with the alternative ECDS2, whereas the alternative ECDS1 ranked second when using the TOPSIS method.

Generally speaking, the alternative ECDS2 was the best-ranked when using all the approaches (as seen in Figure 2), although some deviations in the ranking orders obtained by using different approaches were expected. Possible deviations in the ranking orders obtained by using different approaches are caused by the differences and specificities of the calculation procedures applied in different approaches, whereas deviations usually reflect in the case of worse-ranked alternatives. the alternative ECDS2, whereas the alternative ECDS1 ranked second when using the TOPSIS method. Generally speaking, the alternative ECDS2 was the best-ranked when using all the approaches (as seen in Figure 2), although some deviations in the ranking orders obtained by using different approaches were expected. Possible deviations in the ranking orders obtained by using different approaches are caused by the differences and specificities of the calculation procedures applied in different approaches, whereas deviations usually reflect in the case of worse-ranked alternatives.

in Tables 8 and 9. The difference occurs with the alternative ECDS3, which now shared first place with

*Symmetry* **2020**, *12*, x FOR PEER REVIEW 12 of 16

**Table 13.** The ranking by using the score function and the cosine similarity measure.

 **Overall Ratings Score Rank Cosine Rank**  ECDS1 <0.55, 0.00, 0.00> 0.78 3 0.55 3 ECDS2 <1.00, 0.00, 0.00> 1.00 1 1.00 1 ECDS3 <1.00, 0.00, 0.00> 1.00 1 1.00 1

**Figure 2.** Ranking results achieved by utilizing different procedures. **Figure 2.** Ranking results achieved by utilizing different procedures.
