Passenger Satisfaction Evaluation of Public Transportation Using Pythagorean Fuzzy MULTIMOORA Method under Large Group Environment
Abstract
:1. Introduction
2. Literature Review
3. Preliminaries
- (1)
- (2)
- (3)
- (4)
- (1)
- If, then;
- (2)
- If, then;
- (3)
- If, then.
4. The Proposed Methodology
- (1)
- is the set of rail transit lines in a rail transit network, where denotes the ith line, I = 1, 2, …, m.
- (2)
- is the set of passenger satisfaction evaluation criteria determined for a rail transit network, where denotes the jth criterion, j = 1, 2, …, n.
- (3)
- is the set of m passenger groups, where Gi denotes the passenger group that takes part in the evaluation of , i = 1, 2, …, m.
- (4)
- is the vector of numbers of passengers concerning set G, where represents the number of passengers in group , i = 1, 2, …, m.
- (5)
- is the set of linguistic terms adopted by the passengers for satisfaction evaluation. These linguistic terms can be expressed in PFNs . For example, if a seven-point linguistic term set is used, the linguistic terms can be denoted by PFNs, as shown in Table 1.
- (6)
- is the passenger satisfaction evaluation matrix of rail transit line , where represents the satisfaction evaluation rating provided by the hth passenger from group Gi regarding the jth criterion based on the linguistic term set S, , i = 1, 2, …, m, h = 1, 2, …, , j = 1, 2, …, n.
4.1. Aggregating the Opinions of Large Group Passengers
4.2. Computing the Weights of Evaluation Criteria
4.3. Determining the Ranking of Rail Transit Lines
5. Illustrate Example
5.1. Background
5.2. Application of the Proposed Method
5.3. Discussions
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Linguistic Terms | PFNs |
---|---|
Very good (VG) | (0.80, 0.05) |
Good (G) | (0.05, 0.80) |
Moderately good (MG) | (0.70, 0.15) |
Medium (M) | (0.55, 0.25) |
Moderately poor (MP) | (0.45, 0.40) |
Poor (P) | (0.30, 0.55) |
Very poor (VP) | (0.20, 0.70) |
Linguistic Terms | PFNs |
---|---|
Very important (VI) | (0.95, 0.05) |
Important (I) | (0.80, 0.20) |
Medium (M) | (0.50, 0.50) |
Unimportant (U) | (0.35, 0.65) |
Very unimportant (VU) | (0.05, 0.95) |
Lines | Operating Time | Line Length (km) | Daily Ridership (Ten Thousand) | Trip Time (Minutes) | Number of Stations |
---|---|---|---|---|---|
A1 | 5:30–22:30 | 36.89 | 115.8 | 42 | 28 |
A2 | 5:30–22:45 | 64 | 143.9 | 93 | 30 |
A3 | 5:25–22:30 | 40.3 | 49.1 | 67 | 29 |
A4 | 5:30–22:30 | 33.6 | 76.9 | 55/57 | 26 |
A5 | 5:30–22:30 | 44.35 | 73.5 | 63 | 33 |
Dimensions | Criteria |
---|---|
Assurance | Train Interval (C1) |
Speed of trains (C2) | |
Operating time (C3) | |
The diversity of access to information (C4) | |
Noise level on the trains (C5) | |
Vibration level on the trains (C6) | |
Noise level of the stations (C7) | |
The comfort of the trains (C8) | |
Empathy | Particular people can easily take the subway (C9) |
The convenience of access and use of the trains (C10) | |
Reliability | The smoothness of the train (C11) |
The frequency of train failures (C12) | |
Arrival performance concerning schedules (C13) | |
A sense of security at the station (C14) | |
A sense of security inside trains (C15) | |
Reliability of the information broadcasted in the stations and trains (C16) | |
Responsiveness | Efficiency and quality of the service (C17) |
Politeness and dressing of staff (C18) | |
Tangibles | Lighting quality of stations (C19) |
Cleanliness inside the stations (C20) | |
Lighting quality inside the stations (C21) | |
Temperature and ventilation system of stations and trains (C22) | |
Convenience of vertical elevators and escalators (C23) | |
Convenience of ticket vending machines and ticket gates (C24) | |
Price of tickets (C25) | |
Availability of the seat on the platform (C26) |
Criteria | A1 | A2 | A3 | A4 | A5 |
---|---|---|---|---|---|
C1 | [0.00,0.00,0.09,0.14,0.25,0.32,0.20] | [0.08,0.06,0.13,0.08,0.23,0.20,0.22] | [0.03,0.04,0.06,0.08,0.21,0.36,0.22] | [0.00,0.00,0.00,0.00,0.02,0.45,0.53] | [0.01,0.01,0.02,0.07,0.34,0.31,0.24] |
C2 | [0.00,0.02,0.18,0.11,0.28,0.30,0.11] | [0.06,0.10,0.11,0.03,0.21,0.21,0.29] | [0.05,0.04,0.04,0.08,0.27,0.28,0.23] | [0.00,0.00,0.00,0.06,0.00,0.94,0.00] | [0.01,0.00,0.01,0.11,0.28,0.39,0.20] |
C3 | [0.00,0.00,0.20,0.11,0.26,0.26,0.17] | [0.05,0.09,0.10,0.07,0.24,0.26,0.18] | [0.04,0.04,0.07,0.11,0.28,0.30,0.15] | [0.05,0.05,0.08,0.08,0.09,0.33,0.32] | [0.00,0.04,0.10,0.17,0.17,0.34,0.19] |
… | … | … | … | … | … |
C24 | [0.09,0.13,0.09,0.20,0.19,0.22,0.08] | [0.04,0.15,0.08,0.07,0.14,0.32,0.19] | [0.05,0.06,0.04,0.07,0.28,0.27,0.22] | [0.04,0.07,0.11,0.05,0.18,0.30,0.25] | [0.02,0.02,0.05,0.06,0.31,0.35,0.20] |
C25 | [0.20,0.04,0.10,0.11,0.37,0.18,0.00] | [0.03,0.11,0.10,0.12,0.09,0.27,0.29] | [0.06,0.05,0.04,0.13,0.22,0.23,0.26] | [0.04,0.09,0.08,0.07,0.19,0.29,0.25] | [0.03,0.03,0.06,0.24,0.25,0.30,0.10] |
C26 | [0.08,0.11,0.23,0.08,0.30,0.21,0.00] | [0.04,0.11,0.12,0.11,0.14,0.27,0.23] | [0.08,0.04,0.08,0.12,0.24,0.31,0.13] | [0.04,0.08,0.08,0.10,0.20,0.28,0.23] | [0.02,0.03,0.15,0.18,0.31,0.25,0.07] |
Criteria | A1 | A2 | A3 | A4 | A5 |
---|---|---|---|---|---|
C1 | [0.6518,0.1752] | [0.6133,0.2147] | [0.6601,0.1696] | [0.7571,0.0848] | [0.6693,0.1557] |
C2 | [0.6080,0.2204] | [0.6410,0.1859] | [0.6497,0.1772] | [0.6906,0.1586] | [0.6701,0.1584] |
C3 | [0.6200,0.2059] | [0.6160,0.2139] | [0.6229,0.2061] | [0.6767,0.1544] | [0.6408,0.1897] |
C4 | [0.3197,0.5623] | [0.6500,0.1771] | [0.6644,0.1656] | [0.6370,0.1912] | [0.6548,0.1753] |
C5 | [0.4211,0.4371] | [0.6229,0.2080] | [0.6017,0.2289] | [0.6204,0.2115] | [0.5283,0.3107] |
C6 | [0.4958,0.3619] | [0.6103,0.2213] | [0.6085,0.2210] | [0.6523,0.1767] | [0.5731,0.2595] |
C7 | [0.4175,0.4416] | [0.6340,0.1958] | [0.5982,0.2352] | [0.6315,0.1942] | [0.5665,0.2675] |
C8 | [0.5627,0.2756] | [0.6533,0.1774] | [0.5846,0.2474] | [0.6502,0.1779] | [0.5003,0.3435] |
C9 | [0.5648,0.2688] | [0.6172,0.2141] | [0.5983,0.2329] | [0.6319,0.1987] | [0.5611,0.2775] |
C10 | [0.5620,0.2744] | [0.6153,0.2151] | [0.6333,0.1962] | [0.6349,0.1925] | [0.6394,0.1871] |
C11 | [0.5737,0.2604] | [0.6188,0.2120] | [0.6512,0.1796] | [0.6061,0.2277] | [0.6394,0.1894] |
C12 | [0.6073,0.2230] | [0.6236,0.2111] | [0.6205,0.2080] | [0.6443,0.1870] | [0.6579,0.1679] |
C13 | [0.6131,0.2189] | [0.6315,0.1957] | [0.6346,0.1974] | [0.6461,0.1870] | [0.6842,0.1438] |
C14 | [0.6030,0.2306] | [0.6321,0.1960] | [0.6404,0.1847] | [0.6397,0.1902] | [0.6438,0.1862] |
C15 | [0.5932,0.2385] | [0.6202,0.2116] | [0.6095,0.2248] | [0.6459,0.1829] | [0.6453,0.1849] |
C16 | [0.5897,0.2426] | [0.6367,0.1951] | [0.6425,0.1879] | [0.6354,0.1994] | [0.6429,0.1864] |
C17 | [0.5873,0.2490] | [0.6456,0.1841] | [0.6307,0.1986] | [0.6483,0.1837] | [0.6524,0.1769] |
C18 | [0.6103,0.2190] | [0.6327,0.1987] | [0.6445,0.1832] | [0.6502,0.1785] | [0.6512,0.1782] |
C19 | [0.5957,0.2328] | [0.6071,0.2262] | [0.6535,0.1724] | [0.6339,0.1988] | [0.6846,0.1470] |
C20 | [0.6065,0.2216] | [0.5902,0.2383] | [0.6349,0.2009] | [0.6365,0.1954] | [0.6677,0.1618] |
C21 | [0.6094,0.2193] | [0.6296,0.2009] | [0.6463,0.1805] | [0.6478,0.1828] | [0.6849,0.1452] |
C22 | [0.4966,0.3554] | [0.6375,0.1968] | [0.6398,0.1843] | [0.6560,0.1749] | [0.6297,0.2008] |
C23 | [0.5984,0.2334] | [0.6312,0.2011] | [0.6257,0.2027] | [0.6369,0.1925] | [0.6223,0.2044] |
C24 | [0.5482,0.2941] | [0.6243,0.2103] | [0.6436,0.1835] | [0.6514,0.1778] | [0.6604,0.1669] |
C25 | [0.5044,0.3396] | [0.6501,0.1804] | [0.6429,0.1840] | [0.6466,0.1829] | [0.6044,0.2268] |
C26 | [0.5040,0.3407] | [0.6276,0.2038] | [0.6111,0.2213] | [0.6400,0.1891] | [0.5794,0.2507] |
Criteria | DM1 | DM2 | DM3 | DM4 | DM5 |
---|---|---|---|---|---|
C1 | VI | I | I | VI | I |
C2 | I | VI | I | VI | I |
C3 | M | VI | I | VI | I |
C4 | M | I | VI | I | VU |
C5 | M | I | M | I | VI |
C6 | M | I | M | I | VI |
C7 | U | I | M | VI | M |
C8 | I | VI | M | I | VI |
C9 | M | I | U | VI | U |
C10 | I | VI | I | I | I |
C11 | I | VI | I | VI | I |
C12 | VI | VI | VI | VI | VI |
C13 | I | I | VI | VI | M |
C14 | I | M | I | VI | VI |
C15 | I | VI | I | VI | VI |
C16 | I | M | M | I | I |
C17 | I | I | VI | VI | I |
C18 | I | M | VI | VI | M |
C19 | I | M | VI | VI | I |
C20 | I | M | I | VI | VI |
C21 | I | M | I | M | I |
C22 | I | I | I | M | VI |
C23 | I | VI | I | M | VI |
C24 | I | VI | VI | M | VI |
C25 | M | VI | M | I | M |
C26 | U | VI | M | I | M |
Criteria | Subjective Weights | Objective Weights | Combination Weights |
---|---|---|---|
C1 | 0.0366 | 0.0351 | 0.0334 |
C2 | 0.0370 | 0.0366 | 0.0352 |
C3 | 0.0369 | 0.0377 | 0.0362 |
C4 | 0.0367 | 0.0378 | 0.0361 |
C5 | 0.0363 | 0.0414 | 0.0391 |
C6 | 0.0363 | 0.0402 | 0.0380 |
C7 | 0.0364 | 0.0408 | 0.0387 |
C8 | 0.0376 | 0.0400 | 0.0392 |
C9 | 0.0364 | 0.0400 | 0.0379 |
C10 | 0.0396 | 0.0388 | 0.0400 |
C11 | 0.0417 | 0.0387 | 0.0420 |
C12 | 0.0499 | 0.0380 | 0.0493 |
C13 | 0.0417 | 0.0373 | 0.0404 |
C14 | 0.0376 | 0.0380 | 0.0372 |
C15 | 0.0417 | 0.0385 | 0.0417 |
C16 | 0.0363 | 0.0381 | 0.0359 |
C17 | 0.0417 | 0.0379 | 0.0410 |
C18 | 0.0393 | 0.0376 | 0.0384 |
C19 | 0.0393 | 0.0377 | 0.0385 |
C20 | 0.0376 | 0.0382 | 0.0374 |
C21 | 0.0363 | 0.0372 | 0.0351 |
C22 | 0.0367 | 0.0389 | 0.0371 |
C23 | 0.0376 | 0.0385 | 0.0377 |
C24 | 0.0393 | 0.0382 | 0.0390 |
C25 | 0.0369 | 0.0390 | 0.0375 |
C26 | 0.0364 | 0.0400 | 0.0379 |
Lines | |||
---|---|---|---|
A1 | [0.5648,0.2713] | 0.1107 | [1.80 × 107,0.9557] |
A2 | [0.6277,0.2029] | 0.0417 | [6.11 × 106,0.8095] |
A3 | [0.6308,0.1984] | 0.0386 | [5.41 × 106,0.8175] |
A4 | [0.6485,0.1823] | 0.0186 | [1.23 × 105,0.7723] |
A5 | [0.6328,0.1960] | 0.0377 | [5.37 × 106,0.8285] |
Lines | Ratio System | Reference Point Approach | Full Multiplicative Form | Final Ranking |
---|---|---|---|---|
A1 | 5 | 5 | 5 | 5 |
A2 | 4 | 4 | 3 | 4 |
A3 | 3 | 3 | 2 | 3 |
A4 | 1 | 1 | 1 | 1 |
A5 | 2 | 2 | 4 | 2 |
Lines | Number of Samples | Passenger Satisfaction Score | Frequency of Train Failures |
---|---|---|---|
Line1 | 1925 | 87.43 | 17 |
Line2 | 2359 | 88.00 | 13 |
Line3 | 819 | 88.22 | 10 |
Line4 | 1312 | 89.58 | 3 |
Line7 | 1258 | 89.39 | 2 |
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Li, X.-H.; Huang, L.; Li, Q.; Liu, H.-C. Passenger Satisfaction Evaluation of Public Transportation Using Pythagorean Fuzzy MULTIMOORA Method under Large Group Environment. Sustainability 2020, 12, 4996. https://doi.org/10.3390/su12124996
Li X-H, Huang L, Li Q, Liu H-C. Passenger Satisfaction Evaluation of Public Transportation Using Pythagorean Fuzzy MULTIMOORA Method under Large Group Environment. Sustainability. 2020; 12(12):4996. https://doi.org/10.3390/su12124996
Chicago/Turabian StyleLi, Xu-Hui, Lin Huang, Qiang Li, and Hu-Chen Liu. 2020. "Passenger Satisfaction Evaluation of Public Transportation Using Pythagorean Fuzzy MULTIMOORA Method under Large Group Environment" Sustainability 12, no. 12: 4996. https://doi.org/10.3390/su12124996