# A Comparative Analysis of Homogenous Groups’ Preferences by Using AIP and AIJ Group AHP-PROMETHEE Model

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

- Elaborate on a new model, AIJ–Group AHP–PROMETHEE, to evaluate urban public transport.
- Comparative analysis with the conventional AIP approach to testing the applicability of the new model.
- Sensitivity analysis for the PROMETHEE outputs is possible for the AIJ approach and is not applicable in the case of the AIP approach because of the final aggregation.

## 3. Materials and Methods

#### 3.1. AHP Method

#### 3.2. PROMETHEE Method

#### 3.2.1. PROMETHEE I

_{i}P

^{I}a

_{i}I

^{I}a

_{i}

_{′}

_{i}R

^{I}a

_{i}

_{′}

#### 3.2.2. PROMETHEE II

_{i}P

^{II}a

_{i}

_{′}

_{i}I

^{II}a

_{i}

_{′}

#### 3.3. Aggregation of Individual Priorities

#### 3.4. Aggregation of Individual Judgements

## 4. Results

#### 4.1. The Aggregation of Individual Priorities

#### 4.2. The Aggregation of Individual Judgements

#### 4.3. GAIA Plane and Sensitivity Analysis

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Sensitivity analysis ‘Distance to stop’, (

**a**) criteria weights and (

**b**) alternatives’ rankings.

**Figure 6.**Sensitivity analysis Time to reach stop, (

**a**) criteria weights and (

**b**) alternatives’ rankings.

Reference | Model | Methodology |
---|---|---|

F. Lolli, et al. [37] | Group Fuzzy PROMETHEE | The AIP approach to select the optimum waste treatment |

Jelena J. Stankovic, et al. [50] | PCA–PROMETHEE | Principal component analysis and PROMETHEE method to evaluate the development of the circular economy |

Juan de Ona, et al. [51] | Statistical analysis | A statistical approach to analyze public and private service quality |

Díez–Mesa, et al. [52] | Structural Equation Modelling | Evaluation of Underground mode service quality by using Structural equation modelling approach |

P. Amenta, et al. [53] | Group AHP | The AIJ approach to aggregate decision makers evaluations into a common group preference matrix |

M. Escobar, et al. [33] | Group AHP | The AIP approach for group AHP method |

L. Turcksin, et al. [28] | AHP–PROMETHEE | Combination of two MCDA methods and the exploit of GAIA plane to promote clean fleet factors |

A. Alkharabsheh, et al. [54] | Group AHP | The AIJ group AHP for the evaluation of passenger demand for public transport |

L. Oubahman, et al. [20] | Group PROMETHEE | AIP approach to aggregate the final scores of PROMETHEE method computed for every decision maker |

Hsu–Shih Shih [55] | Group PROMETHEE | The enhancement of threshold determination for a group of decision makers in PROMETHEE I, II and III |

Proposed model | Group AHP–Group PROMETHEE | The AIP approach for the model Group AHP-PROMETHEE The AIJ approach for the model Group AHP-PROMETHEE Comparative analysis between both approaches Cardinal outputs and sensitivity analysis of the AIJ Group AHP-PROMETHEE model, GAIA plane Application of the new model to evaluate urban public transport service quality |

Numerical Values | Verbal Description |
---|---|

1 | Equal importance of both elements |

3 | Moderate importance of one element over another |

5 | Strong importance of one element over another |

7 | Very Strong importance of one element over another |

9 | Absolute importance of one element over another |

2,4,6,8 | Intermediate values |

n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|

RI | 0 | 0 | 0.58 | 0.9 | 1.12 | 1.24 | 1.32 | 1.41 | 1.45 |

Criteria | Adopted Nomination in Figures | Interpretation |
---|---|---|

Service quality | - | All provided services except on-vehicle and information services |

Approachability | - | Line access |

Directness | - | Ability to reach the destination without shifting vehicles |

Reliability | - | Respecting planned schedules |

Time availability | - | Time frame of line operation |

Speed | - | The speed of travelling process |

Distance to stop | Distance | Proximity of origin stations |

Safety of stop | Safety | Subjective feeling |

Comfort in stop | Comfort | Seats, cooling system, heating system |

Need to transfer | Transfer | Need to change the vehicle to reach the destination |

Fit connections | Connections | Time connection between lines to reach the destination |

Frequency of lines | Frequency | Frequency of buses, Trams and Underground modes |

Limited time of use | Limited.time | Time between the first and the last line of a day |

Journey time | Journey.time | The time between on-board and getting off the vehicle |

Awaiting time | Awaiting.time | Waiting time in the station for the line |

Time to reach stop | Time.to.stop | Time to reach the origin station |

AIP | ${\mathit{\phi}}_{\mathit{G}\text{}\left(\mathit{A}\mathit{I}\mathit{P}\right)}^{+}$ | ${\mathit{\phi}}_{\mathit{G}\text{}\left(\mathit{A}\mathit{I}\mathit{P}\right)}^{-}$ | ${\mathsf{\Phi}}_{\mathit{G}\text{}\left(\mathit{A}\mathit{I}\mathit{P}\right)}$ | Ranking |
---|---|---|---|---|

Bus | 0.085018 | 0.252672 | −0.16765 | 3 |

Tram | 0.148229 | 0.130923 | 0.017306 | 2 |

Underground | 0.231249 | 0.080907 | 0.150339 | 1 |

First Level Criteria | Weight | Ranking | Second Level Criteria | Local Weight | Local Ranking | Final Weight | New Ranking |
---|---|---|---|---|---|---|---|

Approachability | 0.13695723 | 5 | Distance to stop | 0.30313998 | 9 | 0.04151721 | 9 |

Safety of stop | 0.58742974 | 1 | 0.08045275 | 7 | |||

Comfort in stop | 0.10943029 | 10 | 0.01498727 | 10 | |||

Directness | 0.20093286 | 3 | Need to transfer | 0.49852044 | 4 | 0.10016914 | 4 |

Fit connections | 0.50147956 | 3 | 0.10076372 | 3 | |||

Time availability | 0.23720442 | 2 | Frequency of lines | 0.45573878 | 5 | 0.10810325 | 2 |

Limited time of use | 0.54426122 | 2 | 0.12910117 | 1 | |||

Speed | 0.25002706 | 1 | Journey time | 0.31907272 | 8 | 0.07977681 | 8 |

Awaiting time | 0.35912068 | 6 | 0.08978989 | 5 | |||

Time to reach stop | 0.3218066 | 7 | 0.08046036 | 6 | |||

Reliability | 0.13981934 | 4 |

AIJ | ${\mathit{\phi}}_{\mathit{G}\text{}\left(\mathit{A}\mathit{I}\mathit{J}\right)}^{+}$ | ${\mathit{\phi}}_{\mathit{G}\text{}\left(\mathit{A}\mathit{I}\mathit{J}\right)}^{-}$ | ${\mathsf{\Phi}}_{\mathit{G}\text{}\left(\mathit{A}\mathit{I}\mathit{J}\right)}$ | Ranking |
---|---|---|---|---|

Bus | 0.0729 | 0.2934 | −0.2205 | 3 |

Tram | 0.1223 | 0.0563 | 0.066 | 2 |

Underground | 0.2274 | 0.0729 | 0.1545 | 1 |

Criteria | Weight Stability Interval | Criteria | Weight Stability Interval |
---|---|---|---|

Distance to stop | [0.00%, 19.08%] | Frequency of lines | [0%, 100%] |

Safety of stop | [0.65%, 100%] | Limited time of use | [0%, 100%] |

Comfort in stop | [0%, 100%] | Journey time | [0%, 100%] |

Need to transfer | [0%, 100%] | Awaiting time | [0%, 100%] |

Fit connections | [0%, 100%] | Time to reach stop | [0%, 23%] |

AIP Approach | AIJ Approach | Net Flow Ratio | |
---|---|---|---|

Bus | −0.16765 | −0.2205 | 0.760317 |

Tram | 0.017306 | 0.066 | 0.262212 |

Underground | 0.150339 | 0.1545 | 0.973068 |

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**MDPI and ACS Style**

Oubahman, L.; Duleba, S.
A Comparative Analysis of Homogenous Groups’ Preferences by Using AIP and AIJ Group AHP-PROMETHEE Model. *Sustainability* **2022**, *14*, 5980.
https://doi.org/10.3390/su14105980

**AMA Style**

Oubahman L, Duleba S.
A Comparative Analysis of Homogenous Groups’ Preferences by Using AIP and AIJ Group AHP-PROMETHEE Model. *Sustainability*. 2022; 14(10):5980.
https://doi.org/10.3390/su14105980

**Chicago/Turabian Style**

Oubahman, Laila, and Szabolcs Duleba.
2022. "A Comparative Analysis of Homogenous Groups’ Preferences by Using AIP and AIJ Group AHP-PROMETHEE Model" *Sustainability* 14, no. 10: 5980.
https://doi.org/10.3390/su14105980