# Assessment Urban Transport Service and Pythagorean Fuzzy Sets CODAS Method: A Case of Study of Ciudad Juárez

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Multicriteria Decision Making

#### 1.2. Weights of the Criteria and Decision Makers

#### The Criteria for Public Transportation

## 2. Basic Concepts of Pythagorean Fuzzy Set

**Definition**

**1.**

**Definition**

**2.**

## 3. The Proposed Methodology

**Step 1.**Identify transport problem.

**Step 2.**Define criteria and alternatives.

**Step 3.**Integrate a group of DMs to assess each criteria.

**Step 4.**Determine the importance of criteria. Using the linguistic terms expressed by pythagorean fuzzy numbers shown in Table 1, the group of DMs analyzes the criteria that describe all alternatives, then all DMs give an evaluation for each criterion to be considered and determine what is the contribution of each one to the problem.

**Step 5.**Construct the Pythagorean Fuzzy decision matrix for alternative assessment. The individual opinion of DMs in linguistic terms is transformed using the linguistic variables of the Table 2, then all opinions of each DM are included in an aggregated Pythagorean Fuzzy decision matrix (APFDM) as follows:

**Step 6.**Calculate the Pythagorean fuzzy normalized matrix using linear normalization. Using Equations (16) and (17) this step is developed as following.

**Step 7.**Calculate the Pythagorean Fuzzy weighted normalized matrix called ${\overline{R}}_{ij}$

**Step 8.**Determine the Pythagorean Fuzzy negative ideal solution $\tilde{ns}$. Using the following equations $\tilde{ns}$ is obtained following:

**Step 9.**Calculate the Pythagorean Fuzzy Euclidean and Taxicab distances. Using alternatives from the negative ideal solution as the following equations:

**Step 10.**Construct the relative assessment matrix based on the Pythagorean Fuzzy Euclidean and Taxicab distances. These steps are given in the following equations:

**Step 11.**Calculate the assessment score of each alternative. In order to obtain the score, Equation (29) is used to determine it:

**Step 12.**Rank the alternatives according to the decreasing values of assessment score $\left({H}_{i}\right)$. The alternative with the highest ${H}_{i}$ is the best alternative among the alternatives.

## 4. Numerical Case

**Stpep 1.**Identify transport problem. This illustrative case belongs to an assessment of public transportation system in Ciudad Juárez, in which several criteria described the principal characteristics that must have a good service to the users.

**Step 2.**Define criteria and alternatives. Table 3 contains the criteria and their explanation—it is very important consider the type of criteria—this means that some criteria are of cost (minimum values are ideal) and another are of benefit (high values are ideal). In order to explain what the alternatives assessment in this proposal are, the modal distribution of public transportation system is in Ciudad Juárez. Here, alternatives assessment in this proposal is described as follows in Table 4:

**Step 3.**Integrate a group of DMs to assess criteria.

**Step 4.**Determine the importance of criteria.

**Step 5.**Construct the Pythagorean Fuzzy decision matrix for alternatives assessment.

**Step 6.**Calculate the Pythagorean fuzzy normalized matrix using linear normalization.

**Step 7.**Calculate the Pythagorean Fuzzy weighted normalized matrix called ${\tilde{R}}_{ij}$. In this mode, the respective matrix ${\tilde{R}}_{ij}$ is presented in Table 9.

**Step 8.**Determine the Pythagorean Fuzzy negative ideal solution (ns).

**Step 9.**Calculate the Pythagorean Fuzzy Euclidean and Taxicab distances. Then, using Equations (24) and (25), the Pythagorean Fuzzy Euclidean and Taxicab distances are described in Table 11 and Table 12. We decide to use Table 5 to explain the meanings of $(R1,\cdots ,R6)$ which represent alternatives involved in this study.

**Step 10**. Construct the relative assessment matrix based on the Pythagorean Fuzzy Euclidean and Taxicab distances.

**Step 11.**Calculate the assessment score of each alternative.

**Step 12.**Rank the alternatives according to the decreasing values of assessment score $\left({H}_{i}\right)$. Finally, the ranking of the alternative is represented as: $R5\succ R1\succ R3\succ R4\succ R6\succ R2$.

## 5. Comparative Analysis

#### Comparative Method

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MCDM | Multicriteria Decision Methods |

PFS | Pythagorean Fuzzy Sets |

FS | Fuzzy Sets |

IFS | Intuitionistic Fuzzy Sets |

IVIFN | Interval-Valued Fuzzy Numbers |

HFLTS | Hesitant Fuzzy Linguistic Term Sets |

IFWA | Intuitionistic Fuzzy Weighted Average |

PFWAA | Pythagorean Fuzzy Weighted Arithmetic Averaging |

${H}_{i}$ | Assessment Score |

GM | Geometric Mean |

SCL | Smart City Logistic |

DMs | Decision Makers |

MODM | Multi-Objective Decision Making |

MADM | Multi-Attribute Decision Making |

TOPSIS | Technique for Order of Preference by Similarity to Ideal Solution |

PF-TOPSIS | Pythagorean Fuzzy TOPSIS |

CODAS | Combinative Distance-Based Assessment |

PF-CODAS | Pythagorean Fuzzy CODAS |

MOORA | Multi-Objective Optimization on the Basis of the Ratio Analysis |

PF-MOORA | MOORA under Pythagorean Fuzzy Environment |

## References

- Nikiforiadis, A.; Ayfantopoulou, G.; Stamelou, A. Assessing the Impact of COVID-19 on Bike-Sharing Usage: The Case of Thessaloniki, Greece. Sustainability
**2020**, 12, 8215. [Google Scholar] [CrossRef] - Macioszek, E.; Świerk, P.; Kurek, A. The Bike-Sharing System as an Element of Enhancing Sustainable Mobility—A Case Study based on a City in Poland. Sustainability
**2020**, 12, 3285. [Google Scholar] [CrossRef] [Green Version] - Macioszek, E.; Kurek, A. The use of a park and ride system—A case study based on the city of Cracow (Poland). Energies
**2020**, 13, 3473. [Google Scholar] [CrossRef] - Politis, I.; Fyrogenis, I.; Papadopoulos, E.; Nikolaidou, A.; Verani, E. Shifting to Shared Wheels: Factors Affecting Dockless Bike-Sharing Choice for Short and Long Trips. Sustainability
**2020**, 12, 8205. [Google Scholar] [CrossRef] - Ibrahim, A.N.H.; Borhan, M.N.; Rahmat, R.A.O. Understanding Users’ Intention to Use Park-and-Ride Facilities in Malaysia: The Role of Trust as a Novel Construct in the Theory of Planned Behaviour. Sustainability
**2020**, 12, 2484. [Google Scholar] [CrossRef] [Green Version] - Liachovičius, E.; Skrickij, V.; Podviezko, A. MCDM Evaluation of Asset-Based Road Freight Transport Companies Using Key Drivers That Influence the Enterprise Value. Sustainability
**2020**, 12, 7259. [Google Scholar] [CrossRef] - Alkharabsheh, A.; Moslem, S.; Duleba, S. Evaluating passenger demand for development of the urban transport system by an AHP model with the real-world application of Amman. Appl. Sci.
**2019**, 9, 4759. [Google Scholar] [CrossRef] [Green Version] - Villa Silva, A.J.; Pérez Dominguez, L.A.; Martínez Gómez, E.; Alvarado-Iniesta, A.; Pérez Olguín, I.J.C. Dimensional analysis under pythagorean fuzzy approach for supplier selection. Symmetry
**2019**, 11, 336. [Google Scholar] [CrossRef] [Green Version] - Perez, L.; Alvarado-Iniesta, A.; Rodríguez-Borbón, I.; Vergara, O. Intuitionistic fuzzy MOORA for supplier selection. DYNA
**2015**, 82, 34–41. [Google Scholar] [CrossRef] - Cal y Mayor y Asociados. Estudio Integral para el Corredor de Transporte Público “Corredor Tecnológico”, Informe 3: Factibilidad del trazo; Cal y Mayor y Asociados, Escala. 2015. Available online: https://www.imip.org.mx/imip/files/sites/pdus2016/Anexos/EstudioIntegralCorredordeTransportePublicoTecnologico/REPORT3.PDF (accessed on 1 May 2019).
- Karel, W.; Brauers, W.; Zavadskas, E. The MOORA method and its application to privatization in a transition economy. Control Cybern.
**2006**, 35, 445–469. [Google Scholar] - Flores-Ruvalcaba, A.A.; Pérez-Domínguez, L.; García-Villalba, L.A.; Almeraz-Durán, S. Una comparación entre el método MOORA y CODAS bajo ambiente de Conjunto Pitagoreano Difuso. Rev. De Innovación Sist.
**2019**, 3, 9–19. [Google Scholar] [CrossRef] - Keshavarz-Ghorabaee, M.; Zavadskas, E.K.; Turskis, Z.; Antucheviciene, J. A new combinative distance-based assessment (CODAS) method for multi-criteria decision-making. Econ. Comput. Econ. Cybern. Stud. Res./Acad. Econ. Stud.
**2016**, 50, 25–44. [Google Scholar] - Aznar Bellver, J.; Guijarro Martínez, F. Nuevos métodos de Valoración. Modelos Multicriterio; Editorial Universitat Politècnica de València: València, Spain, 2012. [Google Scholar]
- Zavadskas, E.; Turskis, Z.; Kildiene, S. State of art surveys of overviews on MCDM/MADM methods. Technol. Econ. Dev. Econ.
**2014**, 20, 165–179. [Google Scholar] [CrossRef] [Green Version] - Penadés Plà, V. Aplicación de la Toma de Decisión Multi-Criterio al Diseño Sostenible de Puentes de Hormigón. Master’s Thesis, Universitat Politècnica de València, Valencia, Spain, 2017. [Google Scholar]
- Keyvan Ekbatani, M.; Cats, O. Multi-criteria appraisal of multi-modal urban public transport systems. In Transportation Research Procedia, Proceedings of the 18th Euro Working Group on Transportation, EWGT 2015, Delft, The Netherlands, 14–16 July 2015; Elsevier: Amsterdam, The Netherlands, 2015; pp. 1–11. [Google Scholar]
- Vahdani, B.; Mousavi, S.M.; Tavakkoli-Moghaddam, R.; Hashemi, H. A new design of the elimination and choice translating reality method for multi-criteria group decision-making in an intuitionistic fuzzy environment. Appl. Math. Model.
**2013**, 37, 1781–1799. [Google Scholar] [CrossRef] - Duleba, S. An AHP-ISM approach for considering public preferences in a public transport development decision. Transport
**2019**, 34, 662–671. [Google Scholar] [CrossRef] [Green Version] - Saaty, T.L. What is the analytic hierarchy process? In Mathematical Models for Decision Support; Springer: Berlin/Heidelberg, Germany, 1988; pp. 109–121. [Google Scholar]
- Hwang, C.L.; Yoon, K. Methods for multiple attribute decision making. In Multiple Attribute Decision Making; Springer: Berlin/Heidelberg, Germany, 1981; pp. 58–191. [Google Scholar]
- Ceballos, B.; Lamata, M.; Pelta, D.; Sánchez, J. El método TOPSIS relativo vs. absoluto. Recta
**2013**, 14, 181–192. [Google Scholar] - Opricovic, S. Multicriteria optimization of civil engineering systems. Fac. Civ. Eng. Belgrade
**1998**, 2, 5–21. [Google Scholar] - Nassereddine, M.; Eskandari, H. An integrated MCDM approach to evaluate public transportation systems in Tehran. Transp. Res. Part A Policy Pract.
**2017**, 106, 427–439. [Google Scholar] [CrossRef] [Green Version] - Roy, B. Classement et choix en présence de points de vue multiples. Rev. Française D’informatique Et De Rech. Opérationnelle
**1968**, 2, 57–75. [Google Scholar] [CrossRef] - Ghorabaee, M.K.; Amiri, M.; Zavadskas, E.K.; Hooshmand, R.; Antuchevičienė, J. Fuzzy extension of the CODAS method for multi-criteria market segment evaluation. J. Bus. Econ. Manag.
**2017**, 18, 1–19. [Google Scholar] [CrossRef] [Green Version] - Panchal, D.; Chatterjee, P.; Shukla, R.; Choudhury, T.; Tamosaitiene, J. Integrated fuzzy AHP-CODAS framework for maintenance decision in urea fertilizer industry. Econ. Comput. Econ. Cybern. Stud. Res.
**2017**, 51, 179–196. [Google Scholar] - Badi, I.; Abdulshahed, A. A case study of sypplier selection for a steelmaking company in Libya by using the combinative distance-based assessment (CODAS) model. Decis. Making Appl. Manag. Eng.
**2018**, 1, 1–12. [Google Scholar] [CrossRef] - Boltürk, E. Pythagorean fuzzy CODAS and its application to supplier selection in a manufacturing firm. J. Enterp. Inf. Manag.
**2018**, 31. [Google Scholar] [CrossRef] - Peng, X.; Garg, H. Algorithms for interval-valued fuzzy soft sets in emergency decision making based on WDBA and CODAS with new information measure. Comput. Ind. Eng.
**2018**, 119, 439–452. [Google Scholar] [CrossRef] [PubMed] - Badi, I.; Ballem, M.; Shetwan, A. Site selection of desalination plant in Libya by using Combinative Distance-Based Assessment (CODAS) method. Int. J. Qual. Res.
**2018**, 12, 609–624. [Google Scholar] [CrossRef] - Dahooei, J.; Zavadskas, E.; Vanaki, A.; Firoozfar, H.; Keshavarz-Ghorabaee, M. An evaluation model of business intelligence for enterprise systems with new extension of CODAS (CODAS-IVIF). EAM Ekon. Manag.
**2018**, 21, 171–187. [Google Scholar] - Pamučar, D.; Badi, I.; Sanja, K. A Novel Approach for the Selection of Power-Generation Technology Using a Linguistic Neutrosophic CODAS Method: A Case Study in Libya. Energies
**2018**, 11, 2489. [Google Scholar] [CrossRef] [Green Version] - Roy, J.; Das, S.; Kar, S.; Pamučar, D. An extension of the CODAS approach using interval-valued intuitionistic fuzzy set for sustainable material selection in construction projects with incomplete weight information. Symmetry
**2019**, 11, 393. [Google Scholar] [CrossRef] [Green Version] - Yalcin, N.; Yapıcı Pehlivan, N. Application of the Fuzzy CODAS Method Based on Fuzzy Envelopes for Hesitant Fuzzy Linguistic Term Sets: A Case Study on a Personnel Selection Problem. Symmetry
**2019**, 11, 493. [Google Scholar] [CrossRef] [Green Version] - Sansabas-Villalpando, V.; Pérez-Olguín, I.J.C.; Pérez-Domínguez, L.A.; Rodríguez-Picón, L.A.; Mendez-González, L.C. CODAS HFLTS Method to Appraise Organizational Culture of Innovation and Complex Technological Changes Environments. Sustainability
**2019**, 11, 7045. [Google Scholar] [CrossRef] [Green Version] - Ijadi Maghsoodi, A.; Maghsoodi, A.; Poursoltan, P.; Antucheviciene, J.; Turskis, Z. Dam construction material selection by implementing the integrated SWARA-CODAS approach with target-based attributes. Arch. Civ. Mech. Eng.
**2019**, 19, 1194–1210. [Google Scholar] [CrossRef] - Buyukozkan, G.; Göçer, F. Prioritizing the Strategies to Enhance Smart City Logistics by Intuitionistic Fuzzy CODAS. In Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (EUSFLAT 2019), Prague, Czech Republic, 9–13 September 2019; Atlantis Press: Amsterdam, The Netherlands, 2019; pp. 805–811. [Google Scholar]
- Laha, S.; Biswas, S. A hybrid unsupervised learning and multi-criteria decision making approach for performance evaluation of Indian banks. Accounting
**2019**, 5, 169–184. [Google Scholar] [CrossRef] - Karaşan, A.; Boltürk, E.; Kahraman, C. A novel neutrosophic CODAS method: Selection among wind energy plant locations. J. Intell. Fuzzy Syst.
**2019**, 36, 1–14. [Google Scholar] [CrossRef] - Ijadi Maghsoodi, A.; Rasoulipanah, H.; Martínez López, L.; Liao, H.; Zavadskas, E.K. Integrating interval-valued multi-granular 2-tuple linguistic BWM-CODAS approach with target-based attributes: Site selection for a construction project. Comput. Ind. Eng.
**2020**, 139, 106147. [Google Scholar] [CrossRef] - Dahooie, J.H.; Vanaki, A.S.; Mohammadi, N. Choosing the Appropriate System for Cloud Computing Implementation by Using the Interval-Valued Intuitionistic Fuzzy CODAS Multiattribute Decision-Making Method (Case Study: Faculty of New Sciences and Technologies of Tehran University). IEEE Trans. Eng. Manag.
**2019**, 67, 1–14. [Google Scholar] [CrossRef] - Zhou, J.; Li, K.W.; Baležentis, T.; Streimikiene, D. Pythagorean fuzzy combinative distance-based assessment with pure linguistic information and its application to financial strategies of multi-national companies. Econ. Res.-Ekon. Istraživanja
**2020**, 33, 974–998. [Google Scholar] [CrossRef] - Perez, L.; Rodríguez-Picón, L.; Alvarado-Iniesta, A.; Cruz, D.; Xu, Z. MOORA under Pythagorean Fuzzy Set for Multiple Criteria Decision Making. Complexity
**2018**, 2018, 1–10. [Google Scholar] [CrossRef] - Akram, M.; Dudek, W.A.; Dar, J.M. Pythagorean Dombi fuzzy aggregation operators with application in multicriteria decision-making. Int. J. Intell. Syst.
**2019**, 34, 3000–3019. [Google Scholar] [CrossRef] - Ortúzar, J.d.D. Modelos de Demanda de Transporte; Ediciones UC: Villarrica, Chile, 2012. [Google Scholar]
- Zheng, R.; Xu, Y.; Wang, W.; Ning, G.; Bi, Y. Spatial transmission of COVID-19 via public and private transportation in China. Travel Med. Infect. Dis.
**2020**, 34, 101626. [Google Scholar] [CrossRef] - Mogaji, E. Impact of COVID-19 on transportation in Lagos, Nigeria. Transp. Res. Interdiscip. Perspect.
**2020**, 6, 100154. [Google Scholar] [CrossRef] - Tirachini, A.; Cats, O. COVID-19 and public transportation: Current assessment, prospects, and research needs. J. Public Transp.
**2020**, 22, 1. [Google Scholar] [CrossRef] - Mavi, R.K.; Zarbakhshnia, N.; Khazraei, A. Bus rapid transit (BRT): A simulation and multi criteria decision making (MCDM) approach. Transp. Policy
**2018**, 72, 187–197. [Google Scholar] [CrossRef] - Jain, D.S.; Aggarwal, P.; Kumar, P.; Singhal, S.; Sharma, P. Identifying public preferences using multi-criteria decision making for assessing the shift of urban commuters from private to public transport: A case study of Delhi. Transp. Res. Part F Traffic Psychol. Behav.
**2014**, 24, 60–70. [Google Scholar] [CrossRef] [Green Version] - Celik, E.; Bilisik, O.N.; Erdogan, M.; Gumus, A.T.; Baracli, H. An integrated novel interval type-2 fuzzy MCDM method to improve customer satisfaction in public transportation for Istanbul. Transp. Res. Part E: Logist. Transp. Rev.
**2013**, 58, 28–51. [Google Scholar] [CrossRef] - Akram, M.; Dudek, W.A.; Ilyas, F. Group decision-making based on pythagorean fuzzy TOPSIS method. Int. J. Intell. Syst.
**2019**, 34, 1455–1475. [Google Scholar] [CrossRef] - Han, Q.; Li, W.; Song, Y.; Zhang, T.; Wang, R. A new method for MAGDM based on improved TOPSIS and a novel pythagorean fuzzy soft entropy. Symmetry
**2019**, 11, 905. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Pythagorean Fuzzy (PF)- combinative distance-based assessment (CODAS) Methodology (Source: The authors).

Linguistic Terms | $\mathit{\mu}$ | $\mathit{\nu}$ | $\mathit{\pi}$ |
---|---|---|---|

Apprentice (Ap )/Very Unimportant (VU) | 0.10 | 0.90 | 0.42 |

Learner (Lr)/Unimportant (U) | 0.35 | 0.60 | 0.72 |

Capable (Cp )/Medium (M) | 0.50 | 0.45 | 0.74 |

Skillful (S) /Important (I) | 0.75 | 0.40 | 0.53 |

Dominant (D)/Very Important (VI) | 0.90 | 0.10 | 0.42 |

Linguistic Terms | $\mathit{\mu}$ | $\mathit{\nu}$ | $\mathit{\pi}$ |
---|---|---|---|

Extremenly Low (EL) | 0.10 | 0.99 | 0.10 |

Very Low (VL) | 0.10 | 0.97 | 0.22 |

Low (L) | 0.25 | 0.92 | 0.30 |

Medium Low (ML) | 0.40 | 0.87 | 0.29 |

Medium (M) | 0.50 | 0.80 | 0.33 |

Medium High (MH) | 0.60 | 0.71 | 0.37 |

High (H) | 0.70 | 0.60 | 0.39 |

Very High (VH) | 0.80 | 0.44 | 0.41 |

Extremenly High (EH) | 1.00 | 0.00 | 0.00 |

Criteria | Reference |
---|---|

Average travel time, Convenience, Security, Reliability, Flexibility, Precision, Operational risk, Quality of service, Energy consumption, Available, Accessibility | [50] |

Timeliness, Average travel time, Convenience, Intramodality, Security, cost, System coverage, Service timetable, Reliability, Velocity, Comfortable, Available, Mobility impact | [17] |

Frequency, Security, Cost, Comfortable and Accessibility | [51] |

Timeliness, Average travel time, Cost, System coverage | [24] |

Cost, Occupancy, Comfortable, Accessibility, Information | [52] |

Visual information of COVID-19 of mask, Training protocols of COVID-19, identify safe seats | [49] |

Line | Ramal | Status | Alternatives |
---|---|---|---|

1-A | Paseo de la Victoria (Express) | In service | R1 |

1-A | Morelos | In service | R2 |

1-A | Unitec | In service | R3 |

1-A | Tradicional | In service | R4 |

1-B | Talamas (Express) | In service | R5 |

Universitaria | Universitaria | In service | R6 |

Decision Maker | 1 | 2 |
---|---|---|

Linguistic Term | D | Ap |

PF number | {$0.90$, $0.10$, $0.42$} | {$0.10$, $0.90$, $0.42$} |

Criteria | Description | Type | DM1 | DM2 | ${\mathit{\mu}}_{\mathit{k}}$ | ${\mathit{\nu}}_{\mathit{k}}$ | ${\mathit{\pi}}_{\mathit{k}}$ | W(${\mathit{\lambda}}_{\mathit{j}}$) |
---|---|---|---|---|---|---|---|---|

C1 | Frequency | Benefit | VI | I | 0.8908 | 0.1149 | 0.4397 | 0.0453 |

C2 | Timeliness | Benefit | I | M | 0.7337 | 0.4047 | 0.5458 | 0.0384 |

C3 | Average travel time | Cost | VI | I | 0.8908 | 0.1149 | 0.4397 | 0.0453 |

C4 | Convenience | Benefit | I | M | 0.7337 | 0.4047 | 0.5458 | 0.0384 |

C5 | Intramodality | Benefit | M | VI | 0.5884 | 0.3872 | 0.7098 | 0.0360 |

C6 | Security | Benefit | VI | M | 0.8843 | 0.1162 | 0.4522 | 0.0454 |

C7 | Cost | Cost | VI | VI | 0.9000 | 0.1000 | 0.4243 | 0.0453 |

C8 | System coverage | Benefit | M | M | 0.5000 | 0.4500 | 0.7399 | 0.0315 |

C9 | Service timetable | Benefit | M | M | 0.5000 | 0.4500 | 0.7399 | 0.0315 |

C10 | Reliability | Benefit | VI | VI | 0.9000 | 0.1000 | 0.4243 | 0.0453 |

C11 | Velocity | Cost | VI | VI | 0.9000 | 0.1000 | 0.4243 | 0.0453 |

C12 | Occupancy | Benefit | I | I | 0.7500 | 0.4000 | 0.5268 | 0.0387 |

C13 | Flexibility | Benefit | M | M | 0.5000 | 0.4500 | 0.7399 | 0.0315 |

C14 | Precision | Benefit | M | M | 0.5000 | 0.4500 | 0.7399 | 0.0315 |

C15 | operational risk | Cost | VI | VI | 0.9000 | 0.1000 | 0.4243 | 0.0453 |

C16 | Comfortable | Benefit | I | I | 0.7500 | 0.4000 | 0.5268 | 0.0387 |

C17 | Quality of service | Benefit | I | I | 0.7500 | 0.4000 | 0.5268 | 0.0387 |

C18 | Energy consumption | Benefit | VI | VI | 0.9000 | 0.1000 | 0.4243 | 0.0453 |

C19 | Mobility impact | Benefit | VI | VI | 0.9000 | 0.1000 | 0.4243 | 0.0453 |

C20 | Available | Benefit | M | M | 0.5000 | 0.4500 | 0.7399 | 0.0315 |

C21 | Accessibility | Benefit | VI | VI | 0.9000 | 0.1000 | 0.4243 | 0.0453 |

C22 | Information in stations | Benefit | M | M | 0.5000 | 0.4500 | 0.7399 | 0.0315 |

C23 | Visual information on buses | Benefit | I | M | 0.7337 | 0.4047 | 0.5458 | 0.0384 |

C24 | Protocols of COVID-19 | Benefit | VI | I | 0.8908 | 0.1149 | 0.4397 | 0.0453 |

C25 | Identify safe seats and place | Benefit | VI | M | 0.8843 | 0.1162 | 0.4522 | 0.0454 |

Criteria | R1 | R2 | R3 | R4 | R5 | R6 | R1 | R2 | R3 | R4 | R5 | R6 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

C1 | H | MH | MH | M | MH | VH | M | MH | H | H | MH | VH |

C2 | VL | L | L | L | VL | VL | M | ML | L | M | VL | M |

C3 | ML | M | ML | M | H | VH | L | M | VH | MH | H | VH |

C4 | MH | M | M | MH | MH | H | H | M | M | M | ML | MH |

C5 | M | MH | MH | M | L | L | ML | MH | M | M | L | M |

C6 | M | MH | H | ML | MH | ML | M | MH | H | ML | MH | ML |

C7 | H | H | H | H | H | ML | H | H | H | H | H | ML |

C8 | M | H | MH | MH | ML | M | M | H | H | M | ML | M |

C9 | M | ML | M | MH | ML | L | M | M | M | M | ML | L |

C10 | ML | M | MH | ML | ML | H | ML | M | MH | ML | ML | H |

C11 | L | H | M | MH | M | M | MH | H | MH | MH | VH | VH |

C12 | MH | M | M | L | MH | H | H | M | M | L | H | VH |

C13 | MH | L | VL | VL | VL | L | H | L | VL | M | L | L |

C14 | MH | H | M | MH | ML | L | MH | MH | M | H | ML | L |

C15 | VH | M | M | M | ML | MH | VH | M | H | M | M | H |

C16 | ML | M | ML | M | L | L | M | M | MH | M | L | M |

C17 | M | MH | M | ML | ML | ML | MH | MH | ML | M | MH | MH |

C18 | ML | MH | M | M | ML | M | ML | MH | M | M | ML | M |

C19 | H | H | H | H | MH | MH | MH | H | H | H | MH | MH |

C20 | ML | M | ML | H | ML | H | ML | M | ML | M | M | H |

C21 | L | MH | ML | MH | VL | L | M | MH | M | MH | VL | M |

C22 | VL | M | MH | ML | VH | VH | VL | M | M | ML | M | M |

C23 | ML | ML | ML | ML | L | M | ML | M | ML | M | M | M |

C24 | MH | M | M | ML | ML | MH | M | ML | ML | ML | ML | M |

C25 | EL | L | ML | L | L | VL | VL | M | L | L | L | VL |

(a) | ||||||||||||||||||

Alternative | C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | |||||||||

$\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | |

R1 | $0.857$ | $0.713$ | $0.668$ | $0.953$ | $1.000$ | $1.000$ | $0.885$ | $0.874$ | $0.819$ | $0.880$ | $0.714$ | $0.750$ | $0.571$ | $0.690$ | $0.714$ | $0.750$ | $0.845$ | $0.898$ |

R2 | $0.750$ | $0.620$ | $0.935$ | $0.992$ | $0.776$ | $0.914$ | $0.723$ | $0.763$ | $1.000$ | $1.000$ | $0.857$ | $0.845$ | $0.571$ | $0.690$ | $1.000$ | $1.000$ | $0.696$ | $0.833$ |

R3 | $0.765$ | $0.630$ | $0.867$ | $0.986$ | $0.813$ | $0.929$ | $0.723$ | $0.763$ | $0.986$ | $0.988$ | $1.000$ | $1.000$ | $0.571$ | $0.690$ | $0.874$ | $0.859$ | $0.845$ | $0.898$ |

R4 | $0.660$ | $0.566$ | $1.000$ | $1.000$ | $0.759$ | $0.904$ | $0.855$ | $0.849$ | $0.833$ | $0.888$ | $0.571$ | $0.690$ | $0.571$ | $0.690$ | $0.845$ | $0.835$ | $1.000$ | $1.000$ |

R5 | $0.750$ | $0.620$ | $0.347$ | $0.935$ | $0.555$ | $0.686$ | $0.846$ | $0.842$ | $0.417$ | $0.772$ | $0.857$ | $0.845$ | $0.571$ | $0.690$ | $0.571$ | $0.690$ | $0.676$ | $0.826$ |

R6 | $1.000$ | $1.000$ | $0.668$ | $0.953$ | $0.485$ | $0.503$ | $1.000$ | $1.000$ | $0.481$ | $0.783$ | $0.571$ | $0.690$ | $1.000$ | $1.000$ | $0.714$ | $0.750$ | $0.423$ | $0.781$ |

(b) | ||||||||||||||||||

Alternative | C10 | C11 | C12 | C13 | C14 | C15 | C16 | C17 | C18 | |||||||||

$\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | |

R1 | 0.571 | 0.690 | 1.000 | 1.000 | 0.859 | 0.833 | 1.000 | 1.000 | 0.868 | 0.859 | 0.515 | 0.510 | 0.823 | 0.927 | 0.853 | 0.898 | 0.667 | 0.816 |

R2 | 0.714 | 0.750 | 0.446 | 0.669 | 0.702 | 0.727 | 0.409 | 0.759 | 1.000 | 1.000 | 0.823 | 0.927 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |

R3 | 0.857 | 0.845 | 0.611 | 0.882 | 0.702 | 0.727 | 0.163 | 0.720 | 0.723 | 0.763 | 0.780 | 0.901 | 0.854 | 0.938 | 0.819 | 0.880 | 0.833 | 0.888 |

R4 | 0.571 | 0.690 | 0.521 | 0.792 | 0.351 | 0.632 | 0.315 | 0.734 | 0.885 | 0.874 | 0.823 | 0.927 | 1.000 | 1.000 | 0.686 | 0.823 | 0.833 | 0.888 |

R5 | 0.571 | 0.690 | 0.568 | 0.841 | 0.859 | 0.833 | 0.203 | 0.724 | 0.578 | 0.701 | 1.000 | 1.000 | 0.500 | 0.870 | 0.712 | 0.833 | 0.667 | 0.816 |

R6 | 1.000 | 1.000 | 0.568 | 0.841 | 1.000 | 1.000 | 0.409 | 0.759 | 0.361 | 0.663 | 0.673 | 0.809 | 0.577 | 0.882 | 0.712 | 0.833 | 0.833 | 0.888 |

(c) | ||||||||||||||||||

Alternative | C19 | C20 | C21 | C22 | C23 | C24 | C25 | |||||||||||

$\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | |||||

R1 | 0.988 | 0.983 | 0.571 | 0.690 | 0.481 | 0.783 | 0.128 | 0.482 | 0.800 | 0.920 | 1.000 | 1.000 | 0.258 | 0.886 | ||||

R2 | 1.000 | 1.000 | 0.714 | 0.750 | 1.000 | 1.000 | 0.639 | 0.584 | 0.823 | 0.927 | 0.831 | 0.891 | 0.743 | 0.964 | ||||

R3 | 1.000 | 1.000 | 0.571 | 0.690 | 0.686 | 0.823 | 0.756 | 0.650 | 0.800 | 0.920 | 0.831 | 0.891 | 1.000 | 1.000 | ||||

R4 | 1.000 | 1.000 | 0.979 | 0.972 | 1.000 | 1.000 | 0.511 | 0.537 | 0.823 | 0.927 | 0.676 | 0.826 | 0.644 | 0.951 | ||||

R5 | 0.857 | 0.845 | 0.588 | 0.695 | 0.167 | 0.732 | 1.000 | 1.000 | 0.577 | 0.882 | 0.676 | 0.826 | 0.644 | 0.951 | ||||

R6 | 0.857 | 0.845 | 1.000 | 1.000 | 0.481 | 0.783 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 0.258 | 0.902 |

(a) | ||||||||||||||||||

CriteriaAlternative | C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | |||||||||

$\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | |

R1 | 0.241 | 0.985 | 0.150 | 0.998 | 1.000 | 1.000 | 0.239 | 0.995 | 0.198 | 0.995 | 0.179 | 0.987 | 0.133 | 0.983 | 0.149 | 0.991 | 0.197 | 0.997 |

R2 | 0.192 | 0.979 | 0.277 | 1.000 | 0.202 | 0.996 | 0.167 | 0.990 | 1.000 | 1.000 | 0.242 | 0.992 | 0.133 | 0.983 | 1.000 | 1.000 | 0.144 | 0.994 |

R3 | 0.198 | 0.979 | 0.228 | 0.999 | 0.218 | 0.997 | 0.167 | 0.990 | 0.347 | 1.000 | 1.000 | 1.000 | 0.133 | 0.983 | 0.211 | 0.995 | 0.197 | 0.997 |

R4 | 0.160 | 0.975 | 1.000 | 1.000 | 0.195 | 0.995 | 0.222 | 0.994 | 0.204 | 0.996 | 0.133 | 0.983 | 0.133 | 0.983 | 0.196 | 0.994 | 1.000 | 1.000 |

R5 | 0.192 | 0.979 | 0.070 | 0.997 | 0.128 | 0.983 | 0.217 | 0.993 | 0.083 | 0.991 | 0.242 | 0.992 | 0.133 | 0.983 | 0.111 | 0.988 | 0.138 | 0.994 |

R6 | 1.000 | 1.000 | 0.150 | 0.998 | 0.110 | 0.969 | 1.000 | 1.000 | 0.097 | 0.991 | 0.133 | 0.983 | 1.000 | 1.000 | 0.149 | 0.991 | 0.079 | 0.992 |

(b) | ||||||||||||||||||

CriteriaAlternative | C10 | C11 | C12 | C13 | C14 | C15 | C16 | C17 | C18 | |||||||||

$\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | |

R1 | 0.133 | 0.983 | 1.000 | 1.000 | 0.225 | 0.993 | 1.000 | 1.000 | 0.207 | 0.995 | 0.118 | 0.970 | 0.207 | 0.997 | 0.221 | 0.996 | 0.162 | 0.991 |

R2 | 0.178 | 0.987 | 0.100 | 0.982 | 0.161 | 0.988 | 0.076 | 0.991 | 1.000 | 1.000 | 0.224 | 0.997 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |

R3 | 0.242 | 0.992 | 0.145 | 0.994 | 0.161 | 0.988 | 0.029 | 0.990 | 0.152 | 0.992 | 0.204 | 0.995 | 0.222 | 0.998 | 0.205 | 0.995 | 0.229 | 0.995 |

R4 | 0.133 | 0.983 | 0.119 | 0.989 | 0.071 | 0.982 | 0.057 | 0.990 | 0.217 | 0.996 | 0.224 | 0.997 | 1.000 | 1.000 | 0.156 | 0.992 | 0.229 | 0.995 |

R5 | 0.133 | 0.983 | 0.132 | 0.992 | 0.225 | 0.993 | 0.036 | 0.990 | 0.113 | 0.989 | 1.000 | 1.000 | 0.105 | 0.995 | 0.164 | 0.993 | 0.162 | 0.991 |

R6 | 1.000 | 1.000 | 0.132 | 0.992 | 1.000 | 1.000 | 0.076 | 0.991 | 0.066 | 0.987 | 0.164 | 0.990 | 0.125 | 0.995 | 0.164 | 0.993 | 0.229 | 0.995 |

(c) | ||||||||||||||||||

CriteriaAlternative | C19 | C20 | C21 | C22 | C23 | C24 | C25 | |||||||||||

$\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | |||||

R1 | 0.395 | 0.999 | 0.111 | 0.988 | 0.109 | 0.989 | 0.023 | 0.977 | 0.196 | 0.997 | 1.000 | 1.000 | 0.056 | 0.994 | ||||

R2 | 1.000 | 1.000 | 0.149 | 0.991 | 1.000 | 1.000 | 0.128 | 0.983 | 0.206 | 0.997 | 0.227 | 0.995 | 0.189 | 0.998 | ||||

R3 | 1.000 | 1.000 | 0.111 | 0.988 | 0.169 | 0.991 | 0.162 | 0.987 | 0.196 | 0.997 | 0.227 | 0.995 | 1.000 | 1.000 | ||||

R4 | 1.000 | 1.000 | 0.309 | 0.999 | 1.000 | 1.000 | 0.097 | 0.981 | 0.206 | 0.997 | 0.165 | 0.991 | 0.155 | 0.998 | ||||

R5 | 0.242 | 0.992 | 0.115 | 0.989 | 0.036 | 0.986 | 1.000 | 1.000 | 0.124 | 0.995 | 0.165 | 0.991 | 0.155 | 0.998 | ||||

R6 | 0.242 | 0.992 | 1.000 | 1.000 | 0.109 | 0.989 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 0.056 | 0.995 |

(a) | ||||||||||||||||||

Criteria | C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | |||||||||

$\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | |

ns | 1.000 | 0.975 | 1.000 | 0.997 | 0.110 | 1.000 | 1.000 | 0.990 | 1.000 | 0.991 | 1.000 | 0.983 | 0.133 | 1.000 | 1.000 | 0.988 | 1.000 | 0.992 |

(b) | ||||||||||||||||||

Criteria | C10 | C11 | C12 | C13 | C14 | C15 | C16 | C17 | C18 | |||||||||

$\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | |

ns | 1.000 | 0.983 | 0.100 | 1.000 | 1.000 | 0.982 | 1.000 | 0.990 | 1.000 | 0.987 | 0.118 | 1.000 | 1.000 | 0.995 | 1.000 | 0.992 | 1.000 | 0.991 |

(c) | ||||||||||||||||||

Criteria | C19 | C20 | C21 | C22 | C23 | C24 | C25 | |||||||||||

$\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | $\mathbf{\mu}$ | $\mathbf{\nu}$ | |||||

ns | 1.000 | 0.992 | 1.000 | 0.988 | 1.000 | 0.986 | 1.000 | 0.977 | 1.000 | 0.995 | 1.000 | 0.991 | 1.000 | 0.994 |

(a) | |||||||||

C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | |

R1 | 0.576 | 0.723 | 0.792 | 0.580 | 0.643 | 0.675 | 0.000 | 0.724 | 0.645 |

R2 | 0.653 | 0.523 | 0.009 | 0.693 | 0.000 | 0.575 | 0.000 | 0.000 | 0.733 |

R3 | 0.644 | 0.596 | 0.012 | 0.693 | 0.427 | 0.000 | 0.000 | 0.623 | 0.645 |

R4 | 0.706 | 0.000 | 0.007 | 0.606 | 0.633 | 0.751 | 0.000 | 0.646 | 0.000 |

R5 | 0.653 | 0.865 | 0.001 | 0.613 | 0.842 | 0.575 | 0.000 | 0.790 | 0.743 |

R6 | 0.001 | 0.723 | 0.001 | 0.000 | 0.815 | 0.751 | 0.751 | 0.724 | 0.849 |

(b) | |||||||||

C10 | C11 | C12 | C13 | C14 | C15 | C16 | C17 | C18 | |

R1 | 0.751 | 0.810 | 0.601 | 0.000 | 0.628 | 0.001 | 0.629 | 0.606 | 0.702 |

R2 | 0.675 | 0.000 | 0.704 | 0.854 | 0.000 | 0.011 | 0.000 | 0.000 | 0.000 |

R3 | 0.575 | 0.002 | 0.704 | 0.942 | 0.720 | 0.007 | 0.605 | 0.632 | 0.595 |

R4 | 0.751 | 0.000 | 0.863 | 0.889 | 0.614 | 0.011 | 0.000 | 0.712 | 0.595 |

R5 | 0.751 | 0.001 | 0.601 | 0.929 | 0.787 | 0.778 | 0.801 | 0.698 | 0.702 |

R6 | 0.000 | 0.001 | 0.000 | 0.854 | 0.872 | 0.002 | 0.766 | 0.698 | 0.595 |

(c) | |||||||||

C19 | C20 | C21 | C22 | C23 | C24 | C25 | |||

R1 | 0.367 | 0.790 | 0.794 | 0.955 | 0.646 | 0.000 | 0.892 | ||

R2 | 0.000 | 0.724 | 0.000 | 0.761 | 0.630 | 0.597 | 0.657 | ||

R3 | 0.000 | 0.790 | 0.691 | 0.702 | 0.646 | 0.597 | 0.000 | ||

R4 | 0.000 | 0.477 | 0.000 | 0.815 | 0.630 | 0.697 | 0.714 | ||

R5 | 0.575 | 0.783 | 0.930 | 0.001 | 0.767 | 0.697 | 0.714 | ||

R6 | 0.575 | 0.000 | 0.794 | 0.001 | 0.000 | 0.000 | 0.892 |

(a) | |||||||||

C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | |

R1 | 0.748 | 0.850 | 0.890 | 0.756 | 0.797 | 0.818 | 0.017 | 0.848 | 0.799 |

R2 | 0.804 | 0.721 | 0.088 | 0.833 | 0.009 | 0.749 | 0.017 | 0.012 | 0.854 |

R3 | 0.798 | 0.770 | 0.105 | 0.833 | 0.644 | 0.017 | 0.017 | 0.782 | 0.799 |

R4 | 0.840 | 0.003 | 0.081 | 0.774 | 0.791 | 0.867 | 0.017 | 0.798 | 0.008 |

R5 | 0.804 | 0.930 | 0.002 | 0.779 | 0.917 | 0.749 | 0.017 | 0.889 | 0.860 |

R6 | 0.025 | 0.850 | 0.031 | 0.010 | 0.903 | 0.867 | 0.867 | 0.848 | 0.921 |

(b) | |||||||||

C10 | C11 | C12 | C13 | C14 | C15 | C16 | C17 | C18 | |

R1 | 0.867 | 0.900 | 0.765 | 0.010 | 0.785 | 0.030 | 0.790 | 0.775 | 0.838 |

R2 | 0.818 | 0.018 | 0.834 | 0.923 | 0.013 | 0.103 | 0.005 | 0.008 | 0.009 |

R3 | 0.749 | 0.039 | 0.834 | 0.971 | 0.844 | 0.082 | 0.775 | 0.792 | 0.767 |

R4 | 0.867 | 0.009 | 0.929 | 0.942 | 0.775 | 0.103 | 0.005 | 0.844 | 0.767 |

R5 | 0.867 | 0.024 | 0.765 | 0.964 | 0.885 | 0.882 | 0.895 | 0.835 | 0.838 |

R6 | 0.017 | 0.024 | 0.018 | 0.923 | 0.934 | 0.037 | 0.875 | 0.835 | 0.767 |

(b) | |||||||||

C19 | C20 | C21 | C22 | C23 | C24 | C25 | |||

R1 | 0.599 | 0.889 | 0.888 | 0.977 | 0.802 | 0.009 | 0.944 | ||

R2 | 0.008 | 0.848 | 0.014 | 0.866 | 0.792 | 0.769 | 0.807 | ||

R3 | 0.008 | 0.889 | 0.826 | 0.829 | 0.802 | 0.769 | 0.006 | ||

R4 | 0.008 | 0.680 | 0.014 | 0.899 | 0.792 | 0.835 | 0.842 | ||

R5 | 0.758 | 0.885 | 0.964 | 0.023 | 0.876 | 0.835 | 0.842 | ||

R6 | 0.758 | 0.012 | 0.888 | 0.023 | 0.005 | 0.009 | 0.943 |

Route | R1 | R2 | R3 | R4 | R5 | R6 |
---|---|---|---|---|---|---|

R1 | 0.000 | 0.845 | 0.370 | 0.478 | −0.137 | 0.546 |

R2 | −0.845 | 0.000 | −0.476 | −0.368 | −0.982 | −0.299 |

R3 | −0.370 | 0.476 | 0.000 | 0.108 | −0.507 | 0.176 |

R4 | −0.478 | 0.368 | −0.108 | 0.000 | −0.615 | 0.068 |

R5 | 0.137 | 0.982 | 0.507 | 0.615 | 0.000 | 0.683 |

R6 | −0.546 | 0.299 | −0.176 | −0.068 | −0.683 | 0.000 |

Route | ${\mathit{H}}_{\mathit{i}}$ | RANK |
---|---|---|

R1 | 2.101 | 2 |

R2 | −2.970 | 6 |

R3 | −0.116 | 3 |

R4 | −0.765 | 4 |

R5 | 2.925 | 1 |

R6 | −1.175 | 5 |

Row 1 | Row 2 | Row 3 | Row 4 | Row 5 | Row 6 | |
---|---|---|---|---|---|---|

R1 | 1 | |||||

R2 | −0.9718 | 1 | ||||

R3 | 0.0107 | −0.0476 | 1 | |||

R4 | −0.9430 | 0.8985 | −0.0652 | 1 | ||

R5 | 0.9628 | −0.9665 | −0.0251 | −0.9569 | 1 | |

R6 | −0.9573 | 0.9080 | −0.0651 | 0.9680 | −0.9622 | 1 |

PF-CODAS Entropy | PF-MOORA | PF-TOPSIS | |
---|---|---|---|

PF-MOORA | $-0.486$ | ||

PF-TOPSIS | $-0.829$ | $0.714$ | |

PF-CODAS propose | $1.000$ | $-0.486$ | $-0.829$ |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Pérez-Dominguez, L.; Durán, S.-N.A.; López, R.R.; Pérez-Olguin, I.J.C.; Luviano-Cruz, D.; Gómez, J.A.H.
Assessment Urban Transport Service and Pythagorean Fuzzy Sets CODAS Method: A Case of Study of Ciudad Juárez. *Sustainability* **2021**, *13*, 1281.
https://doi.org/10.3390/su13031281

**AMA Style**

Pérez-Dominguez L, Durán S-NA, López RR, Pérez-Olguin IJC, Luviano-Cruz D, Gómez JAH.
Assessment Urban Transport Service and Pythagorean Fuzzy Sets CODAS Method: A Case of Study of Ciudad Juárez. *Sustainability*. 2021; 13(3):1281.
https://doi.org/10.3390/su13031281

**Chicago/Turabian Style**

Pérez-Dominguez, Luis, Sara-Nohemí Almeraz Durán, Roberto Romero López, Iván Juan Carlos Pérez-Olguin, David Luviano-Cruz, and Jesús Andrés Hernández Gómez.
2021. "Assessment Urban Transport Service and Pythagorean Fuzzy Sets CODAS Method: A Case of Study of Ciudad Juárez" *Sustainability* 13, no. 3: 1281.
https://doi.org/10.3390/su13031281