V2: Increase in revenue from ticket sales (Figure <sup>6</sup> right): *T = f(T1, T2, T3, ….. , Tn)→*min (1)

o V2: Increase in revenue from ticket sales (Figure 6 right):

$$P\_1 = f(P\_{11}, P\_{12}, P\_{13}, \dots, P\_{1n}) \to \max \tag{2}$$

where *P* denotes revenue. where *P* denotes revenue.

**Figure 6.** V1—reduction in operating costs, V2—increase in revenue from ticket sales. **Figure 6.** V1—reduction in operating costs, V2—increase in revenue from ticket sales. **Figure 7.** V3—increase in ticket revenue and reduction in operating costs, V4—increase in revenue

o V5: Increase in revenue from PSO services and reduction in operating costs (Figure 8 left):

o V3: Increase in ticket revenue and reduction in operating costs (Figure 7 left): # V3: Increase in ticket revenue and reduction in operating costs (Figure <sup>7</sup> left): from Public Service Obligation (PSO) services.

$$P\_1 = f(P\_{11}, P\_{12}, P\_{13}, \dots, P\_{1n}) \to \text{max.} \land T = f(T\_1, T\_2, T\_3, \dots, T\_n) \to \min \tag{3}$$

*P1 + P2= f(P11, P12, P13, …, P1n) + = f(P21, P22, P23, …, P2n)→*max (6)

*P2 = f(P21, P22, P23, ….. , P1n)→*max (4) o V6: Increase in revenue from ticket sales and PSO services (Figure 8 right): # V4: Increase in revenue from PSO services (Figure <sup>7</sup> right):

in revenue from ticket sales and PSO services.

3.4.2. Identification of Evaluation Criteria

increase in revenues under the PSO contract.

$$P\_2 = f(P\_{21}, P\_{22}, P\_{23}, \dots, \dots, P\_{1n}) \to \max \tag{4}$$

**Figure 8.** V5—increase in revenue from PSO services and reduction in operating costs, V6—increase

**Figure 9.** V7—increase in revenue from ticket sales and PSO services and reduction in costs.

Identification and quantification of the criteria for evaluating the manner of implementing the principles and concluding a PSO contract were carried out over four steps: Defining the required level or volume of service, reduction in business costs, increase in revenues from ticket sales, and

The selection of an optimal variant depends on many factors. Therefore, in the proposed methodology, as the criteria, the following values have been adopted: The reality of the feasibility of

o V7: Increase in revenue from ticket sales and PSO services and reduction in costs (Figure 9):

*P1 + P2= f(P11, P12, P13, …, P1n) + = f(P21, P22, P23, …, P2n)→*max (7)

[37,38].

*3.4. Forming a MCDM Model* 

variants are described in [36]:

o V1: Reduction in operating costs (Figure 6 left):

o V2: Increase in revenue from ticket sales (Figure 6 right):

3.4.1. Possible Solutions

where *T* denotes costs.

where *P* denotes revenue.

**Figure 6.** V1—reduction in operating costs, V2—increase in revenue from ticket sales.

*P1 = f(P11, P12, P13, ….. , P1n)→*max. ˄*T = f(T1, T2, T3, ….. , Tn)→*min (3)

*P2 = f(P21, P22, P23, ….. , P1n)→*max (4)

o V3: Increase in ticket revenue and reduction in operating costs (Figure 7 left):

o V4: Increase in revenue from PSO services (Figure 7 right):

In this paper, a new integrated F-PIPRECIA-F-EDAS model is created for solving problems. Multi-criteria methods for decision-making are used to resolve a large number of problems in all spheres of business, and they represent an area that is developing rapidly, primarily due to a large number of methods that have been developed, particularly within the last decade. The combination of these methods with fuzzy logic gives excellent results because classical methods cannot, with such precision, perform the required quantification, and this is where fuzzy logic shows all its advantages

In order to resolve the problem, seven realistically possible variants (V) have been identified. All

*T = f(T1, T2, T3, ….. , Tn)→*min (1)

*P1 = f(P11, P12, P13, ….. , P1n)→*max (2)

**Figure 7.** V3—increase in ticket revenue and reduction in operating costs, V4—increase in revenue from Public Service Obligation (PSO) services. *Symmetry* **2020**, *12*, x FOR PEER REVIEW 9 of 20 **Figure 7.** V3—increase in ticket revenue and reduction in operating costs, V4—increase in revenue *Symmetry* **2020**, *12*, x FOR PEER REVIEW 9 of 20

o V5: Increase in revenue from PSO services and reduction in operating costs (Figure 8 left):

o V5: Increase in revenue from PSO services and reduction in operating costs (Figure 8 left):

**Figure 7.** V3—increase in ticket revenue and reduction in operating costs, V4—increase in revenue
