assignment of *ςdmk* (*ai*) = *φnet*(*ai*). *3.3. PROSA-C Method for GDSS*

The last, third stage is to use the PROSA-C method [35] in order to identify alternatives that represent the best compromise between decision makers. At this stage, the set of criteria *C* = {*c*1, *c*2,..., *cn*} is replaced by the sequence set *R* = {*Rdm*1, *Rdm*2,..., *RdmK*}. Each *k*-th sequence corresponds to the results of the evaluation of alternatives by the *k*-th decision-maker and is composed of the values *ςdmk* (*ai*) determined in the second stage, i.e., *Rdmk* = *ςdmk* (*a*1), *ςdmk* (*a*2),..., *ςdmk* (*am*) . The performance table *E* = *R*(*A*) is built on the basis of the sets *A* and *R*. The PROSA-C method for GDSS consists of eight steps, with the initial four steps being based on the PROMETHEE II method.

#### **Step 1. Calculating deviations based on pair-wise comparisons.**

The results obtained in the second stage by the individual alternatives are compared for each *k*-th decision maker. For each comparison, the deviation *dk ai*, *aj* is determined, according to Formula (11):

$$d\_k(a\_i, a\_j) = \mathfrak{g}^k(a\_i) - \mathfrak{g}^k(a\_j), \ \forall i, j = 1, \dots, m, \ \forall k = 1, \dots, K \tag{11}$$

#### **Step 2. Calculating the value of the preferences.**

To transform the deviation *dk* into the normalized preference value *Pk* ∈ [0, 1], the V-shaped criterion is used (12):

$$P\_k(a\_i, a\_j) = \begin{cases} 0, & \text{for } d\_k(a\_i, a\_j) \le 0 \\ \frac{d\_k(a\_i, a\_j)}{p\_k}, & \text{for } 0 < d\_k(a\_i, a\_j) \le 2 \\\ 1, & \text{for } d\_k(a\_i, a\_j) > 2 \end{cases}, \forall i, j = 1, \dots, m, \ \forall k = 1, \dots, K \tag{12}$$

The expression *dk ai*, *aj* > 2 can only be true if the PROSA-C or PROSA-G method with the compensation factor *s* > 0.3 was used in the second PROSA GDSS stage.

#### **Step 3. Calculating net outranking flows for individual criteria.**

The net outranking flow of the alternative *ai* over each other alternative for the *k*-th decision maker is calculated, based on Formula (13):

$$\Phi\_k(a\_i) = \frac{1}{m-1} \sum\_{j=1}^{m} \left[ P\_k(a\_i, a\_j) - P\_k(a\_j, a\_i) \right], \forall i = 1, \dots, m, \ \forall k = 1, \dots, K \tag{13}$$

#### **Step 4. Calculating the global net outranking flow.**

For each alternative, a global net outranking flow is computed. The calculations are based on the individual outranking flows of each *k*-th decision-maker and its weight *ωk*, according to Formula (14):

$$\phi\_{net}(a\_i) = \sum\_{k=1}^{K} \phi\_k(a\_i) \,\omega\_{k\prime} \,\forall i = 1, \dots, m \tag{14}$$

#### **Step 5. Analysis of the criteria compensation relationship.**

Determining the values *φk*(*ai*) and *φnet*(*ai*) allows investigating the compensation relations that exist between the alternatives.


The occurrence of the *Cd* or *Cs* relation means that the evaluation of the alternative *ai* by the *k*-th decision maker is not balanced in relation to the other decision makers. The << and >> operators denote the contractual relations as "much less than" and "much greater than", expressing a subjective view of a large difference between the compared values. The ≈ operator expresses the subjective view that the values on both sides of the operator can be considered "approximately equal". The analysis of the compensation relation may be a hint regarding the expected values of the compensation factor *s*. If the decision-maker wants to increase the influence of the balance on the obtained solution, then higher values *s* can be assumed.

#### **Step 6. Calculating absolute deviations for decision makers' assessments.**

The value of the absolute deviation is determined separately for each decision maker and for each alternative, according to Formula (15):

$$AD\_k(a\_i) = |\phi\_{n\ell}(a\_i) - \phi\_k(a\_i)| s\_{k\prime} \,\forall i = 1, \dots, m, \ \forall k = 1, \dots, K \tag{15}$$

where *sk* is the compensation factor for the *k*-th decision maker. In practice, *sk* is a specific weight, and *ADk*(*ai*) is the weighted distance of the global net outranking flow *φnet*(*ai*) from the net outranking flow obtained for the *k*-th decision maker *φk*(*ai*).

#### **Step 7. Calculating individual PROSA values for decision makers' evaluations.**

Individual PROSA values are determined on the basis of Formula (16):

$$PSV\_k(a\_i) = \phi\_k(a\_i) - AD\_k(a\_i), \forall i = 1, \dots, m, \ \forall k = 1, \dots, K \tag{16}$$

#### **Step 8. Calculating the global net PROSA values.**

The net value of PROSA is determined using Formula (17):

$$PSV\_{net}(a\_i) = \sum\_{k=1}^{K} PSV\_k(a\_i)\,\omega\_{k'} \forall i = 1, \dots, m \tag{17}$$

#### *3.4. GAIA Analysis*

An important aspect related to the application of the PROMETHEE and PROSA methods is the GAIA analysis. Formally, it is a method of multi-criteria decision analysis, dealing

with descriptive issues [36]. GAIA aims to provide a complete graphic representation of a decision problem, thanks to which it enables the analysis of the obtained solution and indication of directions for its possible improvement. Therefore, GAIA allows for grasping the decision problem and its solution from a descriptive perspective. It gives the decision maker a clear description of decision alternatives and their consequences [34,37].

In the PROSA GDSS method, the GAIA analysis can be used in stages two and three. In this study, in the second stage, it is based on the values of *φk*(*ai*) (PROMETHEE GAIA) and is used to analyze alternatives in terms of criteria. In the third stage, the GAIA analysis is based on the values of *PSVk*(*ai*) (PROSA-C GAIA), and the analysis concerns the assessments of decision makers. Both PROMETHEE GAIA and PROSA-C GAIA are based on the same procedure and differ only in the input data [38]. The GAIA method can be divided into six steps.

#### **Step 1. Construction of the performance matrix.**

In the performance matrix *M* with dimensions *Mm*×*<sup>n</sup>* (for criteria) or *Mm*×*<sup>K</sup>* (for decision makers), the alternative *ai* is represented by the row *αi*. Each row *α<sup>i</sup>* corresponds to a point *Ai* in space R*<sup>n</sup>* (in the case of criteria) or R*<sup>K</sup>* (in the case of decision makers), so the row *α<sup>i</sup>* contains the coordinates of the point *Ai*. The performance matrix for PROMETHEE GAIA is presented in expression (18), and for PROSA-C GAIA it is presented in expression (19):

$$M = \begin{pmatrix} \phi\_1(a\_1) & \phi\_2(a\_1) & \cdots & \phi\_n(a\_1) \\ \phi\_1(a\_2) & \phi\_2(a\_2) & \cdots & \phi\_n(a\_2) \\ \vdots & \vdots & \ddots & \vdots \\ \phi\_1(a\_m) & \phi\_2(a\_m) & \cdots & \phi\_n(a\_m) \end{pmatrix} = \begin{pmatrix} a\_1 \\ a\_2 \\ \vdots \\ a\_m \end{pmatrix} \tag{18}$$

$$M = \begin{pmatrix} PSV\_1(a\_1) & PSV\_2(a\_1) & \cdots & PSV\_K(a\_1) \\ PSV\_1(a\_2) & PSV\_2(a\_2) & \cdots & PSV\_K(a\_2) \\ \vdots & \vdots & \ddots & \vdots \\ PSV\_1(a\_m) & PSV\_2(a\_m) & \cdots & PSV\_K(a\_m) \end{pmatrix} = \begin{pmatrix} a\_1 \\ a\_2 \\ \vdots \\ a\_m \end{pmatrix} \tag{19}$$

#### **Step 2. Calculating the variance-covariance matrix and determining the GAIA plane.**

The calculation of the variance-covariance matrix is intended to reduce the space R*<sup>n</sup>* (R*K*) to a 2-dimensional plane. In this operation, Formula (20) is used:

$$t\mathbb{C} = M^T \ast M \tag{20}$$

where *t* is the coefficient with a positive integer value, *C* is the variance-covariance matrix, and *T* is the transportation of the *M* matrix. For matrix *C*, the set of eigenvalues *<sup>λ</sup>* = {*λ*1,..., *<sup>λ</sup>n*} or *<sup>λ</sup>* = {*λ*1,..., *<sup>λ</sup>K*} is determined. The plane R<sup>2</sup> is marked by the eigenvectors *u*⊥*v*, corresponding to the two largest eigenvalues from the set *λ* (*λ<sup>u</sup>* and *λv*).

#### **Step 3. Finding coordinates of alternatives.**

Each point *Ai* = (*ui*, *vi*) represents the *<sup>i</sup>*-th alternative in the plane R2. The coordinates of these points are determined according to Formula (21):

$$\begin{cases} u\_i = \mathfrak{a}\_i \* u \\ v\_i = \mathfrak{a}\_i \* v \end{cases} \tag{21}$$

#### **Step 4. Determining the coordinates of the criteria/decision makers' vectors.**

For criteria, each vector <sup>→</sup> *Ck* = *uc <sup>k</sup>*, *<sup>v</sup><sup>c</sup> k* represents the *k*-th criterion on the R<sup>2</sup> plane. In turn, in the case of decision makers, each vector <sup>→</sup> *DMk* = *udm <sup>k</sup>* , *<sup>v</sup>dm k* represents the views of the *k*-th decision maker. The tails of these vectors are at the origin of the coordinate system. The vector coordinates are determined according to Formulas (22) and (23):

$$\begin{cases} u\_k^c = \varepsilon\_k \ast u \\ v\_k^c = \varepsilon\_k \ast v \end{cases} \tag{22}$$

$$\begin{cases} \mu\_k^{dm} = \varepsilon\_k \ast \mathfrak{u} \\ \upsilon\_k^{dm} = \varepsilon\_k \ast \upsilon \end{cases} \tag{23}$$

where *ek* is the *k*-th row of the identity matrix with dimensions *n* × *n* (for criteria) or *K* × *K* (for decision makers).

#### **Step 5. Determining the direction of searching for a compromise solution.**

The vector <sup>→</sup> *π* = [*uπ*, *vπ*] determining the compromise solution is calculated according to Formula (24):

$$\begin{cases} \mu^{\pi} = \mathcal{W} \ast \mathcal{u} \\ v^{\pi} = \mathcal{W} \ast v \end{cases} \tag{24}$$

where *W* is the vector of the normalized weights of criteria (*w*) or decision makers (*ω*).

#### **Step 6. Calculating information loss.**

Reducing the dimensionality of the space R*<sup>n</sup>* (R*K*) to the plane R<sup>2</sup> causes that some information about alternatives and criteria or the views of decision makers is lost. The amount of information transferred to the 2-dimensional space is represented by the *δ* value calculated using Formula (25) or Formula (26), for criteria or decision makers, respectively:

$$\delta^c = \frac{\lambda\_u + \lambda\_v}{\sum\_{k=1}^n \lambda\_k} \tag{25}$$

$$\delta^{dm} = \frac{\lambda\_u + \lambda\_v}{\sum\_{k=1}^{K} \lambda\_k} \tag{26}$$

The GAIA plane provides graphical information on alternatives and criteria or views of decision makers. If the criteria vectors <sup>→</sup> *Ck* (or decision makers vectors <sup>→</sup> *DMk*) point in the same direction, it means that the criteria they represent (views of decision makers) similarly affect the global assessment of alternatives. While the opposite turns of vectors indicate a contradiction of preferences or views. On the other hand, the orthogonal arrangement of vectors means a lack of dependence. The length of a vector is the strength of the influence of a given criterion (decision maker) on the global assessment of alternatives. The further in the plane the point *Ai* representing the *i*-th alternative is in the direction defined by the vector, the more the criterion (decision-maker) represented by the vector supports this alternative. The same principle applies to the vector <sup>→</sup> *π* representing a compromise solution.

#### **4. Results**

#### *4.1. Collection of Alternatives and Criteria, Performance Table of Alternatives*

The first stage of the study was to select decision alternatives and evaluation criteria. The considered alternatives were the most popular e-scooters in Poland. The vehicles for analysis were selected on the basis of information about the most frequently purchased e-scooters. This information was obtained from the three largest stores on the Polish market offering electronic products [39]. The ten most popular vehicles were selected from each store. As some vehicles were included in the top 10 in more than one store, the result was a list of 21 e-scooters that created a set of decision-making alternatives *A*. It is worth noting that the selection of vehicles takes into account the specificity of the Polish market, because e-scooters include three vehicles by Polish manufacturers (Motus and Skymaster).

The selection of criteria was based on literature sources. As the literature shows a shortage of research on the multi-criteria price of e-scooters, the criteria used in similar decision problems concerning e-bikes and e-micromobility in general were analyzed [15,31,32,40,41]. Moreover, publications on a similar problem of choosing an electric car [42–46]. As the criteria in the articles cited are not strictly aligned with the evaluation of e-scooters, only selected criteria were considered in this study. Table 2 contains the criteria selected for the evaluation of e-scooters along with references to the literature.


**Table 2.** Criteria selected for the evaluation of e-scooters.

KERS—Kinetic Energy Recovery System, e-ABS—Electric Anti-lock Braking System.

The analysis of Table 2 shows that not all criteria are based on the literature. In particular, Table 2 defines several criteria closely tailored to the evaluation of e-scooters and related to their specific characteristics. These are criteria for tire diameter, vehicle communication with the mobile application, cruise control, pedestrian mode, presence of a Kinetic Energy Recovery System (KERS) and Electric Anti-lock Braking System (e-ABS), used suspension and braking systems, as well as hill climbing ability and the number of gears (speed modes). Some of the criteria are binary, so they refer to whether a given system/feature is present in the vehicle. Binary criteria occur when, on the basis of information from vehicle manufacturers, it would be difficult to determine which vehicles have for a given system, one that is developed more or less than another. The selected criteria are described using a point scale—these are the criteria for which the quality can be differentiated on the basis of information provided by manufacturers. For example, the braking system can be based on fender, electric, drum, or disk brakes. Depending on the components used in the braking system, it was assigned an appropriate score. In the same way, the use of disk and drum brakes was rewarded, as each of these types of brakes has certain advantages. Disk brakes are more efficient and have more stopping power, but wear faster and require more maintenance than drum brakes. A point scale is also used for the protection rating, depending on the level of protection of the vehicle against solids and liquids. In the case of the price, the lowest amount was selected from among the prices in the three stores from which information on vehicle popularity was obtained. Temporary trade promotions were not taken into account, taking into account only base prices. The underlying criteria (e.g., price, battery charging time, etc.) are described in terms of natural values. Most of the criteria are stimulants, so they are profit criteria [47]. Destimulants, i.e., cost criteria are battery charging time, weight, and price. It should be clarified that the literature often uses the criterion of maximum speed, which, however, was abandoned in this study. The resignation from this criterion is a result of the legal provisions in force in Poland, limiting the maximum permissible speed of e-scooters to 20 km/h [48]. All vehicles under consideration reach this speed and are equipped with a lock that prevents them from

reaching a higher speed. Therefore, the use of the maximum speed criterion in the current legal situation in Poland does not make sense. In this way, a list of 18 evaluation criteria constituting the set of C criteria was obtained and is shown in Table 2.

Table 3 presents the basic information about the e-scooters included in the study and their assessments. Table 3 can also be interpreted as a performance table *E* = *C*(*A*) that is the basis for aggregating the criteria scores.


**Table 3.**

Parameters

 and evaluations

 of e-scooters. #### *4.2. Models of Stakeholder Preferences*

As noted in Section 3.1, the two stakeholders were, respectively:


Of course, the interests and views of these stakeholders are in conflict. The user who rents an e-scooter is primarily interested in safety and comfort when using the vehicle. Therefore, the criteria directly affecting the safety and comfort of driving are of great importance to users: the braking system (including brakes and e-ABS), suspension, or, to a lesser extent, the diameter of the tires. The braking system allows you to stay safe in sudden, unexpected situations while driving. In turn, the suspension system and the diameter of the tires affect the comfort of driving and negotiating unevenness as well as the ability to climb curbs. Equally important are criteria regarding the comfort of use, such as sufficient range, gradeability, number of gears, and cruise control. The range should be sufficient for the needs of a typical user. According to various studies published in the literature, shared e-scooters users cover about 2–4 km in one trip [70,71], and according to other studies, it may even be more than 8 km [72,73]. Taking into account that sometimes you still need to return (e.g., travel from home to work, and then home from work), it may even be over 16 km. It should also be taken into account that as the battery degrades or at lower temperatures, the range will decrease. The ability to climb steep slopes relieves users from having to push the e-scooter uphill when it has too little power to climb the hill. More gears and cruise control allow you to set the right speed and lock it, so that the user can focus on the road and any obstacles. Criteria such as vehicle weight and pedestrian mode are slightly less important. The weight of the vehicle is related to the ease of riding, e.g., in the pedestrian mode. Technical criteria such as battery capacity, engine power, load capacity (assuming that this will be a value greater than the weight of the potential user), the presence of KERS, or protection rating are much less important for the user. However, these criteria are to some (slightly) degree significant, as they are indirectly related to the gradeability, range and failure-free operation of the vehicle. Access to the e-scooter setup via the mobile app is of very little importance, as in the case of a rented e-scooter, only a few users will want to use this feature, and most often the feature will be blocked by the VSS owner. However, battery charging time and price are irrelevant to the VSS customer. The price is irrelevant as the cost of purchasing the vehicle is borne by the owner of the VSS, not the customer. Likewise, the owner of the VSS is responsible for recharging the battery and the customer will not charge it when the battery is depleted, but will simply take another vehicle.

On the other hand, for the VSS owner, the most important criteria are directly related to his actions regarding the handling of e-scooters. From this perspective, criteria such as battery capacity and charging time, KERS, as well as load capacity and protection rating are important. The greater the battery capacity, the less frequently the e-scooter needs to be delivered to the base station and charged. In turn, the longer the charging time, the longer the vehicle is out of use in VSS. For this reason, KERS is to some extent useful as it increases the time intervals between successive charges.

The load capacity should be large enough not to limit the possibility of using the vehicle to obese people, of whom there are, unfortunately, relatively many in Polish society. In turn, the protection rating is a very important criterion determining whether the vehicle must be additionally protected against unfavorable weather conditions. E-scooters are usually left outdoors and are exposed to, for example, rainfall. Therefore, an appropriate degree of protection against liquids ensures their stability of operation, regardless of rainfall. One of the most important criteria for a VSS owner is, of course, the price of the e-scooter. The criteria most important to users are also relatively important, as they are responsible for driving comfort and thus the loyalty and retention of VSS users. Engine power is much less important, which is reflected indirectly in other criteria, and a mobile app is a completely redundant function.

In addition to the weights of criteria, an important aspect of preference modeling is the selection of appropriate preference functions and associated thresholds. The use of a pre-criterion, pseudo-criterion or Gaussian criterion is recommended for quantitative criteria. However, for low grade or quality criteria, consider using a true criterion, semicriterion, or level criterion [74]. In turn, the thresholds *qk*, *pk* and *rk* should be between the reliable values of the minimum and maximum of the *k*-th criterion [74,75]. Taking into account the cited guidelines, the usual preference function was used for the binary criteria and the two-fold number of gears criteria. The level criterion was used for the four-valued tire diameter and load capacity criteria and for the criteria expressed on the 4-point scales (brakes and protection rating). For the remaining criteria, the V-shaped preference functions (pre-criterion and pseudo-criterion) were used. The stakeholder preference models are presented in Table 4.

**Table 4.** Stakeholder preference models.


#### *4.3. Results of E-Scooters Assessment Using the PROSA GDSS Method*

Based on the models of stakeholder preferences and the table of alternative performance, individual stakeholder rankings and group rankings were generated. The value *s*<sup>1</sup> = *s*<sup>2</sup> = 1 was adopted as the compensation factor for the results of the individual assessment in the group procedure. In turn, the weights of the stakeholders were set equal (*ω*<sup>1</sup> = *ω*<sup>2</sup> = 0.5). Table 5 presents the values of *φnet*(*ai*) and ranks obtained in individual rankings, as well as the ranks and values of *PSVnet*(*ai*) obtained in the GDSS procedure.

The analysis of individual rankings in Table 5 shows significant differences in the assessment of e-scooters based on the preferences of individual stakeholders. This is clearly visible on the example of the alternatives A7, A9, A13, A20, which depending on the stakeholder, occupy leading or final positions in the rankings. There is also a significant discrepancy in the case of alternatives A5, A10, A11, A14, A16, and A18, for which the difference between the ratings of the VSS owner and the VSS customer is at least eight positions. These differences are of course due to different stakeholder preferences. One can also observe alternatives that rank similarly or the same in both individual rankings. These are the alternatives A1, A3, A8, and A21. It is easy to notice that the alternatives A1, A8 and A21 occupy the leading positions in the group ranking. Moreover, the A3 and A21 alternatives in the GDSS procedure were ranked higher than it would result from their

position in the individual rankings. This effect is directly related to the PROSA method, which rewards well-balanced alternatives and penalizes unbalanced ones. An example of an alternative which position has been significantly lowered in the group ranking due to a very large discrepancy in individual ranks is A7. The confirmation of most of the indicated observations can be found on the PROMETHEE GAIA plane generated for individual rankings. Due to the fact that both individual rankings are based on the same performance table, the GAIA plant with identically distributed criteria vectors and alternative points is obtained for each of the individual rankings. These solutions differ only in the vector → *π* = [*uπ*, *vπ*] which determines a compromise solution between the criteria. For this reason, both individual solutions are presented on the common PROMETHEE GAIA plant, shown in Figure 3.


**Table 5.** Assessments of alternatives aggregated in individual and PROSA GDSS group rankings.

When analyzing the GAIA plane, it should be noted that not all information was transferred from the R<sup>18</sup> to R<sup>2</sup> space. The value of *δ<sup>c</sup>* = 0.655, so only 65% of the information has been preserved in the two-dimensional space. Nevertheless, some valuable information can be obtained from the figure. On the GAIA plane, the support of criteria for alternatives is clearly visible. For example, criterion *C*<sup>1</sup> strongly supports the alternatives A9, A10, A13 (these vehicles have a very high battery capacity), and criterion *C*<sup>18</sup> supports the alternatives A2, A7, A15, A17, and A20 (these e-scooters have the lowest prices). In addition, it is possible to indicate the solutions most supported by individual stakeholders. The decision maker *dm*<sup>1</sup> strongly supports the alternatives A6, A8, A9, A10, and A13 (the points representing these alternatives are most advanced in the direction indicated by the vector <sup>→</sup> *π*(*dm*1)). In turn, the decision-maker *dm*<sup>2</sup> strongly supports, among others, alternatives A5, A18, A19, A20. On the GAIA plane, the dashed line marks the extension of the vectors <sup>→</sup> *<sup>π</sup>*(*dm*1) and <sup>→</sup> *π*(*dm*2) thus delineating the space of solutions strongly supported by both stakeholders. These solutions include A1, A6, A8 and A21, the four top group ranking alternatives. This analysis shows that the GAIA plane is a valuable carrier of descriptive information about the solution of the decision problem, even if only part of the information was transferred to the plane.

**Figure 3.** PROMETHEE GAIA plane obtained for individual stakeholder rankings.

#### **5. Discussion**

#### *5.1. Comparison of the Results of the PROSA GDSS and PROMETHEE GDSS Methods*

As noted earlier, the PROSA method favors well-balanced (or sustainable) alternatives and penalizes unbalanced ones. In other words, it limits the compensation of factors (criteria, decision makers) in the decision problem. In particular, the PROSA GDSS method limits the compensation of decision makers' assessments at the stage of aggregating individual assessments into group assessments. In this way, PROSA GDSS favors balanced alternatives, assessed at a similar level by all stakeholders.

To analyze the impact of the balance-based approach on solving the decision problem, the results of the PROSA GDSS and PROMETHEE GDSS methods were compared. In accordance with the research procedure presented in Section 3.1, each of these methods was used separately at the stage of aggregating individual assessments into group assessment (PROMETHEE GDSS uses the PROMETHEE II procedure with V-shaped criterion and threshold *pk* = 2 at this stage). Table 6 presents the results of the PROMETHEE GDSS method and the results for the PROSA GDSS method, previously quoted in Table 5. On the other hand, Figure 4 contains the GAIA GDSS planes obtained using the PROMETHEE and PROSA methods (for both planes *δdm* = 1 was obtained).

A comparison of the PROMETHEE GDSS and PROSA GDSS rankings indicates that taking into account the balance between decision makers and limiting compensation significantly changes the rankings of alternatives. Alternative A1, which was ranked second in the PROSA GDSS ranking, without balance (PROMETHEE GDSS ranking), was ranked fifth. In turn, alternative A21 fell from third to seventh, and A4 lost one position (from fifth to sixth). Of the top alternatives, the A8 and A6 retained their ranks. As for the other alternatives, which were penalized for the lack of balance in the PROMETHEE GDSS ranking included unbalanced alternatives, which were penalized for lack of balance in the PROSA GDSS ranking.


**Table 6.** PROMETHEE GDSS and PROSA GDSS groups rankings.

**Figure 4.** GAIA planes obtained for group rankings by aggregating individual rankings using the following methods: (**a**) PROMETHEE GDSS, (**b**) PROSA GDSS.

The differences in the rankings are clearly visible on the GAIA planes based on the PROMETHEE GDSS and PROSA GDSS methods (Figure 4). The vector <sup>→</sup> *π* determining the order of alternatives indicates that in the case of the PROMETHEE GDSS GAIA plane, the leading alternatives are: A8, A10, A9, A1, A6, etc., respectively. On the PROSA GDSS plane, the best alternatives are: A8, A1, A21, A6, A4, etc., respectively. On both GAIA planes, the <sup>→</sup> *π* vectors also correctly indicate the order of the other alternatives. Although the differences in the position of points representing alternatives on both planes of GAIA are small, the position of these points precisely describes the order of alternatives in the rankings and the support of individual alternatives by decision makers. Both GAIA planes indicate that the preferences of decision-makers are independent of each other (they are not supportive, but also not strongly conflicted), as shown by the orthogonal arrangement of the vectors *dm*<sup>1</sup> and *dm*2. These vectors, through their orthogonal arrangement, define the space of solutions constituting a compromise between the two decision-makers. In the case of PROMETHEE GDSS GAIA, this area includes the balanced alternatives A1, A8, A21, and the unbalanced alternative A6, while on the PROSA GDSS GAIA plane, this area covers

only the balanced alternatives A1, A8, A21. This observation confirms that PROSA is able to capture the balance of decision alternatives. It should be noted that the area defined by the vectors *dm*<sup>1</sup> and *dm*<sup>2</sup> is very similar to the area marked in Figure by the extension of the vectors <sup>→</sup> *<sup>π</sup>*(*dm*1) and <sup>→</sup> *π*(*dm*2), which confirms that capturing two individual rankings and their compromise solutions <sup>→</sup> *π* on the GAIA plane can provide relatively precise information about the group solution.

#### *5.2. PROSA GDSS Sensitivity Analysis*

The sensitivity analysis of the PROSA GDSS ranking was considered from two perspectives. We analyzed how the solution of the decision problem changes with linear changes (1) of criteria weights and (2) of the compensation coefficient *sk*. In the first study, the weight of the selected criterion was linearly changed, proportionally increasing or decreasing the initial weights of the remaining criteria. Criterion weights given in Table 4 were used as initial values. Stability ranges of criterion weights were determined on the basis of the sensitivity analysis. Due to the large number of alternatives and the frequent reordering of further positions in the ranking, the stability ranges were derived from the top five alternatives. This makes it possible to determine the stability of the best alternatives without introducing information noise in a situation where changes occur in the last places in the ranking. The stability intervals for each criterion are presented in Table 7. The analysis presented in Table 7 shows that the stability intervals are much wider for the weights defined by the decision maker *dm*<sup>1</sup> than for the weights of the decision maker's criteria *dm*2. This means that the leading alternatives are more sensitive to changes in the weights of the decision maker's criteria *dm*2, while in the case of weight changes by the decision maker *dm*1, the solution is more stable. Table 7 is supplemented by Figure 5 that allows observing the ranking position with linear changes in the weights of individual criteria.


**Table 7.** Stability ranges and sensitivity for the top five positions in the PROSA GDSS ranking.

**Figure 5.** Changes in the PROSA GDSS ranking depending on changes in the weights of the criteria.

The second sensitivity study consisted of a linear change of the value of the compensation coefficient *sk*, separately for decision-makers *dm*<sup>1</sup> and *dm*2. For one of the decision makers, the value of *sk* was changed in the range [0, 1], while for the other stakeholder *sk* = 1 was left. It should be explained that in the case of two-decision makers with equal weights, the change of the coefficient *sk* for *k* = 1 and *k* = 2 gives the same solution. In other words, regardless of the decision-makers for which the *sk* coefficient is changed, the solution will change exactly the same. This is due to the specificity of the PROSA method, because in the case of two decision-makers with the same weights, the solution *φnet*(*ai*) is simply an average. In turn, the distance of both solutions *φk*(*ai*) from the solution *φnet*(*ai*) is the same (*AD*1(*ai*) = *AD*2(*ai*)), which results from Formulas (14) and (15). This is confirmed by Figure 6 showing changes in the PROSA GDSS ranking depending on the

linear change in the value of the *sk* coefficient separately for each of the stakeholders. In this figure, it can be seen that the top five positions in the ranking are stable. The order of the five best alternatives only changes when the value of *sk* for one of the stakeholders drops < 0.5, and for the best three alternatives, when *sk* = 0 for one of the decision makers, bearing in mind that for the other stakeholder *sk* = 1.

**Figure 6.** Changes in the PROSA GDSS ranking depending on changes in the weighting of the criteria.

#### **6. Managerial and Environmental Implications**

The results of the research show that the best compromise between the needs of the VSS owner and the needs of potential users of such a service is the A8—JEEP 2xe Urban Camou. It occupies the leading positions in the individual rankings of both stakeholders, which means that it almost perfectly meets the needs of each of them. Choosing the next good e-scooter is not an obvious decision. If we take into account the need to balance the needs of stakeholders and rely on the methodology taking into account the balance (PROSA GDSS), then the second and third places in the ranking will be occupied by: A1— APRILIA eSR2 and A21—XIAOMI Mi Pro2 2022. However, if we apply the compensation methodology (PROMETHEE GDSS) and we will look for a solution that will be a resultant of the views of both decision makers, without taking into account the balance between them, then the second and third places in the ranking will be occupied by A10—Kaabo Mantis 10 ECO800 and A9—Kaabo Mantis 8. Other good vehicles identified by both methodologies are A6—DUCATI PRO-III 2022, A4—BLAUPUNKT ESC90X and the A1 and A21 vehicles already mentioned in the context of good balance, as well as the A10 previously indicated as a very good solution, although less balanced. All these vehicles largely meet the needs of both the entrepreneur and his customers.

Looking at the problem of choosing e-scooters for VSS in Poland from a broader perspective, one should notice the great potential of business activities related to the provision of this type of service. The introduction of comfortable and eco-friendly e-micromobility vehicles is an opportunity to reduce the unfavorable patterns of daily commuting observed in Poland and the extremely high ratio of private transport [76]. Based on the Recovery and Resilience Plan for Poland (the so-called national recovery plan), it should be noted that from the perspective of the next few years, legal regulations are planned in Poland, which will certainly contribute to an increase in the popularity of e-micromobility and e-mobility. Namely, in the Annex to the Recovery and Resilience Plan for Poland [77] one see that in 2025 in Poland, low-emission transport zones are to be introduced in cities with over

100,000 inhabitants and which exceed pollution standards. In addition, the same annex contains information about new taxes that will be imposed on internal combustion vehicles from 2024 and 2026. Together with the dynamically growing gasoline prices in Poland, these activities will certainly force some vehicle users to give up owning a car and buy their own e-micromobility vehicle or use the VSS.

The development of e-mobility has been supported in Poland for several years, but recently there are also programs promoting the development of e-micromobility. For example, the program of government subsidies for the purchase of electric vehicles ('My electrician') introduced in 2021 in Poland includes co-financing for the purchase of e-cars, but also electric mopeds, motorcycles, and all-terrain vehicles (quads). For vehicles in the L1-L7 categories, a subsidy in the amount of PLN 4000 is planned [78]. In addition, recently Gdynia was the first city in Poland to introduce co-financing for the purchase of e-bikes by residents. The maximum amount of funding is PLN 2500 (not more than 50% of the purchase price) [79].

The basic justification for the indicated trends is the need to reduce environmental pollution, because electric vehicles do not emit exhaust fumes. However, the environmental impact of electric vehicles depends on the country's energy mix. Meanwhile, over 70% of the Polish energy mix is based on carbon [6], which makes the argument about environmental protection lose its sense. According to plans for the Polish energy policy, in the coming years, the Polish energy mix should change to renewable energy sources (mainly offshore wind farms and photovoltaics) and nuclear energy [80], but for now these are mainly plans. Therefore, even if the planned legal regulations and the incentive system were already in force and contributing to an increase in the popularity of electric vehicles in a short time, they can only bring positive environmental effects over a longer time span.

#### **7. Conclusions**

The aim of the article was to analyze selected e-scooters available on the Polish market and to identify vehicles of this type that are most useful from two slightly opposing perspectives—the owner of the VSS and a potential customer of such services. The solution to the given decision problem is of practical value in the presented research. On the other hand, the scientific contribution of the article included the use of the PROSA GDSS method to search for a compromise between the stakeholders of the decision-making process. The results of the PROSA GDSS method were compared with the results of the application of the PROMETHEE GDSS method, which does not take into account the balance between stakeholders, and allows for a strong compensation of decision makers' assessments. Graphical representations of PROSA GDSS and PROMETHEE GDSS solutions on the GAIA plane were also compared. Additionally, an analysis of the sensitivity of the PROSA GDSS ranking, changes in criteria weights, and changes in compensation coefficients was performed. The basic PROSA GDSS solution identified the e-scooter A8—JEEP 2xe Urban Camou as the optimal choice. Both the sensitivity analysis and the solution obtained using the PROMETHEE GDSS method confirmed that it is the optimal alternative, the least sensitive to changes in criteria weights and changes in compensation factors. E-scooters are interesting vehicles, which took a few more places in the PROSA GDSS ranking, because they are vehicles well-balanced between the needs of users and entrepreneurs running VSS.

During the research work, no significant limitations were encountered that could significantly affect the obtained results. There was a problem with obtaining reliable data on individual vehicles, as not all e-scooters manufacturers and suppliers provide complete technical information about vehicles on their websites. Therefore, part of the information was obtained on the basis of an analysis of vehicle operating instructions or reviews of e-scooters posted on the Internet. As for methodological limitations, it should be noted that not all the obtained data were precise and reliable. Therefore, in several cases, an average was entered in the performance table based on information from various sources. Therefore, an interesting direction for further methodological work would be to develop

the PROSA family of methods for fuzzy representations so that they could better capture the uncertainty of the data.

**Author Contributions:** Conceptualization, P.Z.; data curation, P.Z. and I.G.; investigation, P.Z.; methodology, P.Z.; resources, I.G.; supervision, P.Z.; visualization, P.Z.; writing—original draft, P.Z. and I.G.; writing—review & editing, P.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Science Centre, Poland, grant number 2019/35/D/ HS4/02466.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data are contained within the article.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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