# An Integrated Approach of Analytic Hierarchy Process and Triangular Fuzzy Sets for Analyzing the Park-and-Ride Facility Location Problem

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Methodology

## 4. Case Study

## 5. Results

## 6. Discussion

_{2}as a result of the reduction of undesirable trips to the city center caused by the use of private vehicles. However, concerning noise reduction, it is not considered relevant, because currently there is no strong evidence of noise reduction when a P&R system is implemented, and concerning criterion C6.3, using the assumption that green areas can be reduced by implementing the P&R system; although, the P&R system can be developed in combination with green spaces.

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The city of Cuenca Ecuador with the urban areas, Light Rail Line (LRT), and Park and Ride (P&R).

Linguistic Scale of Importance | Scale of Fuzzy Number |
---|---|

Perfect | (8, 9, 10) |

Absolute | (7, 8, 9) |

Very good | (6, 7, 8) |

Fairly good | (5, 6, 7) |

Good | (4, 5, 6) |

Preferable | (3, 4, 5) |

Not bad | (2, 3, 4) |

Weak advantage | (1, 2, 3) |

Equal | (1, 1, 1) |

Criteria Code | Explanation | Description |
---|---|---|

C1 | “Distance” | One of the main parameters for the location of an installation in the P&R system is the distance. |

C1.1 | “Distance from the zones to the P&R system.” | The city is divided into zones that are the origin of the trips through the P&R system. This criterion refers to the distance from the zones to the P&R system. |

C1.2 | “Distance from P&R system to Central Business District.” | Among the distance criteria, it is relevant to consider the distance from the P&R system to the CBD. |

C2 | “Traffic conditions on the route (origin-destination)” | The parameter that is considered to locate a facility is the traffic that exists from the origin to the destination in different periods and through the combination of two modes of transport that allows the P&R system as it is the private vehicle and public transport. |

C2.1 | “Time of travel by private car.” | This is the first part of the trip through the P&R system and represents the time that a user of a private vehicle may spend on the trip. |

C2.2 | “Time of travel by public transport.” | This criterion refers to the second part of the trip that corresponds to the time that the P&R system user spends on public transport until reaching the destination under the conditions of the route. |

C2.3 | “Time of travel by P&R system.” | This criterion refers to the fact that a P&R system can be considered a transport mode that allows a modal shift (private vehicle to public transport); therefore, the travel time through the P&R system depends on the location of the facility. |

C3 | “Accessibility of public transport.” | This parameter is related to public transport and represents one of the P&R systems’ goals: the second part of the trip is through public transport. |

C3.1 | “Frequency of public transport operations.” | Public transport frequency is a factor that determines how accessible the system is. |

C3.2 | “Transfer time from P&R to public transport stop.” | A facility is close to the public transport station; therefore, the modal shift’s transfer time ensures accessibility. |

C3.3 | “The distance of the P&R from the nearest public transport stop.” | The concept of P&R location is that the facilities are close to the public transport stations, the distance from the P&R to the public transport station is a criterion that is considered. |

C4 | “Transport aspects.” | This criterion refers to the P&R system in respect of its essential characteristics within the field of transport. |

C4.1 | “Reduction of trips by private car in CBD.” | A goal that the P&R system achieves when it is implemented is that it reduces private vehicle travel to the CBD. |

C4.2 | “Increase of demand by public transport in CBD.” | The second part of the trip to reach the destination is made through the public transport system, and therefore the demand is increased. |

C4.3 | “Number of public transport connections available.” | The P&R system is connected to public transport, and therefore the connections or lines of public transport is a criterion that allows the success of the system. |

C4.4 | “Demand for parking at a P&R system.” | Demand is the fundamental component to implement any transport system; therefore, this criterion establishes the demand in the P&R system. |

C5 | “Economic” | The economic analysis as a criterion helps to identify how viable the project is. |

C5.1 | “Cost of implementation for the project.” | The criterion refers to the total project cost to implement the P&R system. |

C5.2 | “Cost of land use.” | The cost of land use would change the location of the P&R system. In some cases, it leads to expropriation in areas where there is already a previous building. |

C5.3 | “Cost of the implementation of the telecommunication infrastructure.” | The P&R system needs to report the number of available spots, the connection with public transport, and the system operation; therefore, a cost is the implementation of intelligent transportation systems. |

C5.4 | “Total cost of investment maintenance.” | Maintenance is a cost that leads to ensure that the system is functional over time. |

C6 | “Environmental” | This criterion has emerged in recent years as an essential part of implementing a P&R system. |

C6.1 | “CO_{2} reduction.” | The CO_{2} reduction is based on the criterion that the P&R system allows reducing the undesirable effects of the private vehicle through the decrease of the trips to the CBD. |

C6.2 | “Noise reduction.” | The P&R system allows the reduction of undesirable effects of the P&R system, such as noise reduction. |

C6.3 | “Area occupied by existing green areas.” | This criterion refers to the fact that most P&R systems are implemented in places that are green areas. This is a reduction in green spaces. |

C1 | C2 | C3 | C4 | C5 | C6 | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

C1 | 1 | 1 | 1 | 0.7391 | 0.8511 | 0.9663 | 0.2034 | 0.2269 | 0.2580 | 0.2646 | 0.3020 | 0.3451 | 1.2986 | 1.4777 | 1.6606 | 0.1944 | 0.2154 | 0.2424 |

C2 | 1.0348 | 1.1749 | 1.3529 | 1 | 1 | 1 | 0.2820 | 0.3103 | 0.3443 | 0.2696 | 0.2990 | 0.3335 | 0.2907 | 0.3197 | 0.3549 | 0.2869 | 0.3150 | 0.3488 |

C3 | 3.8763 | 4.4071 | 4.9169 | 2.9044 | 3.2223 | 3.5457 | 1 | 1 | 1 | 2.7121 | 3.0366 | 3.3649 | 2.2264 | 2.5845 | 2.9276 | 3.0695 | 3.4464 | 3.8017 |

C4 | 2.8977 | 3.3107 | 3.7798 | 2.9987 | 3.3450 | 3.7091 | 0.2972 | 0.3293 | 0.3687 | 1 | 1 | 1 | 1.9225 | 2.1637 | 2.3985 | 0.3086 | 0.3512 | 0.4079 |

C5 | 0.6022 | 0.6767 | 0.7701 | 2.8179 | 3.1280 | 3.4402 | 0.3416 | 0.3869 | 0.4492 | 0.4425 | 0.4803 | 0.5330 | 1 | 1 | 1 | 0.2646 | 0.3020 | 0.3451 |

C6 | 4.1249 | 4.6434 | 5.1435 | 2.8666 | 3.1748 | 3.4855 | 0.2630 | 0.2902 | 0.3258 | 2.4518 | 2.8470 | 3.2402 | 2.8977 | 3.3107 | 3.7798 | 1 | 1 | 1 |

**Table 4.**Final aggregated fuzzy comparison matrix (4 $\times $ 4) for the sub-criteria in level 2 (transport aspects branch).

C4.1 | C4.2 | C4.3 | C4.4 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

C4.1 | 1 | 1 | 1 | 0.5627 | 0.6609 | 0.7736 | 1.0428 | 1.2222 | 1.4142 | 4.7524 | 5.7932 | 6.8220 |

C4.2 | 1.2927 | 1.5131 | 1.7771 | 1 | 1 | 1 | 1.3783 | 1.4798 | 1.5874 | 3.2226 | 3.8027 | 4.4302 |

C4.3 | 0.7071 | 0.8182 | 0.9590 | 0.6300 | 0.6758 | 0.7255 | 1 | 1 | 1 | 1.3991 | 1.7180 | 2.0829 |

C4.4 | 0.1466 | 0.1726 | 0.2104 | 0.2257 | 0.2630 | 0.3103 | 0.4801 | 0.5821 | 0.7148 | 1 | 1 | 1 |

**Table 5.**Final aggregated fuzzy comparison matrix (4 $\times $ 4) for the sub-criteria in level 2 (economic branch).

C5.1 | C5.2 | C5.3 | C5.4 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

C5.1 | 1 | 1 | 1 | 0.6310 | 0.6444 | 0.6598 | 1.5157 | 1.5518 | 1.5849 | 0.6310 | 0.6893 | 0.7579 |

C5.2 | 1.5157 | 1.5518 | 1.5849 | 1 | 1 | 1 | 1.2457 | 1.4310 | 1.6345 | 1.7653 | 2.0362 | 2.3199 |

C5.3 | 0.6310 | 0.6444 | 0.6598 | 0.6118 | 0.6988 | 0.8027 | 1 | 1 | 1 | 1.2723 | 1.3933 | 1.5157 |

C5.4 | 1.3195 | 1.4509 | 1.5849 | 0.4310 | 0.4911 | 0.5665 | 0.6598 | 0.7177 | 0.7860 | 1 | 1 | 1 |

**Table 6.**Final aggregated fuzzy comparison matrix (3 $\times $ 3) for the sub-criteria in level 2 (traffic conditions on the route (origin destination) branch).

C2.1 | C2.2 | C2.3 | |||||||
---|---|---|---|---|---|---|---|---|---|

C2.1 | 1 | 1 | 1 | 0.1987 | 0.2329 | 0.2894 | 0.2106 | 0.2506 | 0.3195 |

C2.2 | 3.4553 | 4.2931 | 5.0316 | 1 | 1 | 1 | 0.4928 | 0.5643 | 0.6499 |

C2.3 | 3.1295 | 3.9910 | 4.7484 | 1.5387 | 1.7720 | 2.0294 | 1 | 1 | 1 |

**Table 7.**Final aggregated fuzzy comparison matrix (3 $\times $ 3) for the sub-criteria in level 2 (accessibility of the public transport branch).

C3.1 | C3.2 | C3.3 | |||||||
---|---|---|---|---|---|---|---|---|---|

C3.1 | 1 | 1 | 1 | 4.8914 | 6.0000 | 7.0681 | 2.7865 | 3.4713 | 4.2823 |

C3.2 | 0.1415 | 0.1667 | 0.2044 | 1 | 1 | 1 | 0.3432 | 0.4251 | 0.5493 |

C3.3 | 0.2335 | 0.2881 | 0.3589 | 1.8206 | 2.3522 | 2.9137 | 1 | 1 | 1 |

**Table 8.**Final aggregated fuzzy comparison matrix (3 $\times $ 3) for the sub-criteria in level 2 (environmental branch).

C6.1 | C6.2 | C6.3 | |||||||
---|---|---|---|---|---|---|---|---|---|

C6.1 | 1 | 1 | 1 | 3.3220 | 3.6889 | 4.0357 | 3.3220 | 3.6889 | 4.0357 |

C6.2 | 0.2478 | 0.2711 | 0.3010 | 1 | 1 | 1 | 1.8644 | 2.0396 | 2.2209 |

C6.3 | 0.2478 | 0.2711 | 0.3010 | 0.4503 | 0.4903 | 0.5364 | 1 | 1 | 1 |

Criteria | Weight | Rank |
---|---|---|

C1 | 0.0704 | 5 |

C2 | 0.0645 | 6 |

C3 | 0.3667 | 1 |

C4 | 0.1621 | 3 |

C5 | 0.0961 | 4 |

C6 | 0.2527 | 2 |

Main Criteria | Sub-Criteria | Local Weight | Rank | Global Weight | Rank |
---|---|---|---|---|---|

C1 | C1.1 | 0.8294 | 1 | 0.0584 | 5 |

C1.2 | 0.1706 | 2 | 0.0120 | 18 | |

C2 | C2.1 | 0.1106 | 3 | 0.0071 | 19 |

C2.2 | 0.3738 | 2 | 0.0241 | 13 | |

C2.3 | 0.5334 | 1 | 0.0344 | 11 | |

C3 | C3.1 | 0.6957 | 1 | 0.2551 | 1 |

C3.2 | 0.1063 | 3 | 0.0390 | 8 | |

C3.3 | 0.2232 | 2 | 0.0819 | 3 | |

C4 | C4.1 | 0.3267 | 2 | 0.0530 | 7 |

C4.2 | 0.3794 | 1 | 0.0615 | 4 | |

C4.3 | 0.2197 | 3 | 0.0356 | 9 | |

C4.4 | 0.0906 | 4 | 0.0147 | 17 | |

C5 | C5.1 | 0.2228 | 2 | 0.0214 | 14 |

C5.2 | 0.3569 | 1 | 0.0343 | 12 | |

C5.3 | 0.2180 | 3 | 0.0209 | 15 | |

C5.4 | 0.2076 | 4 | 0.0200 | 16 | |

C6 | C6.1 | 0.6445 | 1 | 0.1628 | 2 |

C6.2 | 0.2225 | 2 | 0.0562 | 6 | |

C6.3 | 0.1385 | 3 | 0.0350 | 10 |

© 2020 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/).

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**MDPI and ACS Style**

Ortega, J.; Tóth, J.; Moslem, S.; Péter, T.; Duleba, S.
An Integrated Approach of Analytic Hierarchy Process and Triangular Fuzzy Sets for Analyzing the Park-and-Ride Facility Location Problem. *Symmetry* **2020**, *12*, 1225.
https://doi.org/10.3390/sym12081225

**AMA Style**

Ortega J, Tóth J, Moslem S, Péter T, Duleba S.
An Integrated Approach of Analytic Hierarchy Process and Triangular Fuzzy Sets for Analyzing the Park-and-Ride Facility Location Problem. *Symmetry*. 2020; 12(8):1225.
https://doi.org/10.3390/sym12081225

**Chicago/Turabian Style**

Ortega, Jairo, János Tóth, Sarbast Moslem, Tamás Péter, and Szabolcs Duleba.
2020. "An Integrated Approach of Analytic Hierarchy Process and Triangular Fuzzy Sets for Analyzing the Park-and-Ride Facility Location Problem" *Symmetry* 12, no. 8: 1225.
https://doi.org/10.3390/sym12081225