*4.6. Hierarchy Structure of the Problem, Based on AHP*

The decision problem hierarchy is formed as shown in Figure 1. The alternatives are at the base, the criteria at the upper level, while the overall goal is at the top.

**Figure 1.** Hierarchy structure of the decision problem.

#### *4.7. Criteria Weighting Based on AHP*

After the formulation of the decision problem hierarchy, 15 criteria pair-wise comparisons (an indicative part is shown in Table 2), were executed by the group of experts, using the 9-level linear Saaty scale (Table 3).




**Table 3.** Relative importance scale for the criteria.

The experts' answers were aggregated by implementing the "aggregation of individual judgments" method, using the geometric mean-GEOM. MEAN (for a set of n numbers x1, x2, ... , xn, geometric mean equals <sup>√</sup><sup>n</sup> x1 <sup>×</sup> x2 ... <sup>×</sup> xn) of the value attributed to each criterion. The AHP consistency ratio (CR: (Equation (3)) is used for the consistency control of the answers. The input data, based on the experts' answers and the geometric mean for each case, can be found in Table 4. When the criterion on the left is selected (Table 2), the value is used for the analysis exactly as it is. When the criterion on the right is selected, the reverse value of the selected one in Table 2 is used for the analysis.

**Table 4.** Expert judgments and geometric mean for the criteria pair-wise comparisons.


The geometric mean values of Table 4 serve as input data for the AHP comparison matrix (Table 5), based on Equation (1), and for the normalized comparison matrix of Table 6, where the calculated criteria priority vector (criteria weights) and the respective consistency control are shown.

**Table 5.** Criteria pair-wise comparison matrix.



**Table 6.** Normalized criteria pair-wise comparison matrix, priority vector (W), and consistency control.

#### *4.8. Evaluation of Alternatives with Regard to Each Criterion, Based on AHP*

The evaluation of the infrastructure alternatives concerning their performance in terms of each criterion is as follows. This is realized through pair-wise comparisons executed by the group of experts. In order to proceed with the pair-wise comparisons of infrastructure alternatives, the same methodological steps as were followed for the criteria pair-wise comparisons were implemented.

Following exactly the same process with the criteria, the alternatives are compared in pairs, using Saaty's 9-level scale, but this time, in terms of preference (Table 7). An indicative part of these pair-wise comparisons (6 pair-wise comparisons for each of the 6 criteria) is shown in Table 8. It should be noted that, in certain cases, in MCA, it might be meaningful to compare two alternatives in terms of a particular criterion, but not in terms of another. When a comparison between two alternatives in terms of a criterion is not meaningful, due to incompatibility or indifference, they are treated as if they were "equal", concerning their performance in terms of this criterion (attributed value: 1) [70].

**Table 7.** Relative preference scale for the alternatives.


**Table 8.** Indicative part of alternatives' pair-wise comparisons.


The input data on the basis of the experts' answers for the infrastructure alternatives pair-wise comparison, as well as the geometric mean for each criterion, are shown in Table 9. The normalized infrastructure alternatives pair-wise comparison matrices, the priority vectors, and the consistency control for each criterion, can be found in Table 10.


**Table 9.** Expert judgments and geometric mean for the alternatives pair-wise comparison, with regard to each criterion.


**Table 10.** Normalized alternatives' pair-wise comparison matrices, priority vectors (W) and consistency control for each criterion.

*4.9. Decision Matrix for the Application of VIKOR and TOPSIS for the Overall Ranking of the Alternatives*

The priority vectors of the alternatives (Table 10), calculated with regard to each criterion with AHP, and showing the ranking of the alternatives for each criterion, serve as input data for the decision matrix, shown in Table 11. This is based on Equation (5), used for the application of VIKOR and TOPSIS, so that the final ranking of the alternatives can be derived. It should be noted that all the criteria are considered as benefit criteria (benefit functions), as the experts were asked which alternative is preferable to the other in the relevant questionnaires.


**Table 11.** Decision matrix for the application of VIKOR and TOPSIS.

*4.10. Application of VIKOR for the Overall Ranking of the Alternatives*

Concerning VIKOR application, the f\* <sup>j</sup> and f−<sup>j</sup> values (Equations (6) and (7)) are calculated on the basis of Table 11:

f \* <sup>j</sup> = maxi(xij) = {0.5780 0.4222 0.3278 0.3475 0.6207 0.4124}

f −<sup>j</sup> = mini(xij) = {0.0477 0.0565 0.0675 0.0702 0.0515 0.1408}

Si, Ri and Qi values for VIKOR (calculated according to Equations (8)–(11), for v = 0.5, adopting the criteria weights (priority vector W) of Table 6, can be found in Table 12. The corresponding ranking of the alternatives (minimum value → best alternative) can be also found in Table 12.

**Table 12.** Si, Ri and Qi values and relevant alternatives' ranking, based on the AHP-VIKOR model.


According to Table 12, the alternative P.C. (lanes dedicated to autonomous electric vehicles with plug-in charging stations beside the road, along the route) has the minimum Qi, so it is first in rank. After checking the satisfaction of the two conditions [32] of the acceptable advantage (0.8879 − 0.000 = 0.8879 > 1/(m − 1) = 1/(4 − 1) = 1/3 = 0.3333) and of the acceptable stability (the alternative P.C. is also first in rank by Si and Ri), the alternative P.C. constitutes the optimum solution of new vehicle technologies in urban areas, according to the AHP-VIKOR model.

#### *4.11. Application of TOPSIS for the Overall Ranking of the Alternatives*

The weighted normalized decision matrix for the application of TOPSIS, shown in Table 13, is calculated on the basis of Table 11, according to Equation (12) and using the criteria weights (priority vector W) of Table 6.

**Table 13.** Weighted normalized decision matrix for TOPSIS application.


The values of A<sup>+</sup> and A<sup>−</sup> for TOPSIS are calculated according to Equations (13)–(14), as follows:

A<sup>+</sup> = {0.0318 0.1777 0.1179 0.0242 0.0261 0.0219}

A− = {0.0026 0.0238 0.0243 0.0049 0.0022 0.0075}

Si +, Si − and ci <sup>+</sup> values (calculated according to Equations (15)–(17)) for TOPSIS, as well as the alternatives ranking (maximum ci <sup>+</sup> value → best alternative), are shown in Table 14.


**Table 14.** Si +, Si − and ci <sup>+</sup> values and alternatives ranking based on the AHP-TOPSIS model.

As shown in Table 14, the alternative P.C. (lanes dedicated to autonomous electric vehicles with plug-in charging stations beside the road, along the route), having the maximum ci +, constitutes the optimum solution for new vehicle technologies in urban areas, according to the AHP-TOPSIS model.

#### *4.12. Reveal of the Optimum Solution*

According to the last step of the methodology described in Section 3, given the convergence (in terms of the optimum solution) of the results derived from the two models, the alternative solution of lanes dedicated to autonomous electric vehicles, with plug-in charging stations beside the road, along the route, constitutes the optimum choice in terms of road infrastructure for autonomous electric vehicles in urban areas, within the framework of safety and sustainability.

#### **5. Results and Discussion**

The application of the two MCA models resulted in the identification of an optimum solution for autonomous electric vehicles in urban areas, integrating safety and sustainability aspects, this being the alternative of lanes dedicated to autonomous electric vehicles with plug-in charging stations beside the road, along the route.

However, apart from the final result, derived as regards the optimum solution, it is also worth commenting on individual results relating to the criteria weighting, as well as to the performance of each alternative in terms of each criterion, derived through the decisionaiding methodology implementation. According to the criteria priority vector shown in Table 6, the criteria related to safety emerge as the most important ones. Specifically, public health, as it relates to electromagnetic radiation, and road safety are highlighted as the most important criteria, with the greatest weights among the other ones (42.07% and 35.95% respectively). Traffic congestion reduction (6.97%), infrastructure cost (5.50%), reduction in natural resources consumption due to low energy loss during charging (5.31%), and charging time (4.20%) are much lower in terms of importance.

According to the alternatives' priority vectors in terms of each criterion, as shown in Table 10, concerning the criteria of construction, operation and maintenance infrastructure cost, the first in ranking is the alternative of a mixed flow of conventional and autonomous electric vehicles, with the alternative of lanes dedicated to autonomous electric vehicles and stationary wireless charging following behind, the alternative of lanes dedicated to autonomous electric vehicles and plug-in charging stations beside the roadway coming next, and the alternative of dedicated lanes to autonomous electric vehicles and dynamic wireless charging along the route being the least preferred alternative for the criterion in question. As regards the criterion of public health related to electromagnetic radiation exposure, the alternatives of mixed flow and separate lanes with stationary plug-in charging are almost together in the first rank, while the alternative of separate lanes with stationary wireless charging follows behind, and the alternative of separate lanes with wireless charging has the lowest performance. Concerning the criterion of road safety, the alternative of a mixed flow has impressively low performance, while it does not make a significant difference for the other three alternatives (dynamic charging seems to have a slightly better performance, due to the fact that vehicle drivers will not have to stop beside the road to charge the vehicle). Concerning the criterion of traffic congestion, the alternative of circulation in separate lanes and dynamic charging comes first, with a significant difference from the last one, which is the mixed flow alternative, while the other two alternatives are in fact almost

together in the second rank. As regards the criterion of charging time, the alternative of dynamic charging holds the first place, with impressively high performance; as expected, mixed flow with charging in existing stations is the least preferred, while separate lanes with plug-in charging and separate lanes with stationary wireless charging are ranked second and third, respectively. Finally, concerning the criterion of energy efficiency related to the charging system, the alternative of separate lanes and dynamic charging is the least preferred, while separate lanes with new plug-in charging stations hold the first place, and mixed flow with charging at existing stations and separate lanes are ranked second and third, respectively (this is to be expected, as energy loss is higher in the case of wireless, and especially dynamic, charging).
