Evaluating Personal Default Risk in P2P Lending Platform: Based on Dual Hesitant Pythagorean Fuzzy TODIM Approach
Abstract
:1. Introduction
2. Preliminaries
2.1. The TODIM Approach
- Step 1.
- Standardize the decision matrix into the matrix .
- Step 2.
- Compute the dominance degree of over each alternative for attribute :
- Step 3.
- Compute the overall value of the alternative by:
- Step 4.
- Rank all the alternatives according to the overall values . Based on this result, we can get the conclusion that the most ideal alternative has largest overall value, and conversely, the worst alternative has the smallest value.
2.2. Dual Pythagorean Hesitant Fuzzy Set
- (1)
- (2)
- (3)
- (4)
- (5)
3. Dual Pythagorean Hesitant Fuzzy TODIM Approach
3.1. Fundamental Knowledge
- (1)
- if, then;
- (2)
- if, then;
3.2. TODIM Method for Dual Hesitant Pythagorean Fuzzy MADM Problems
4. Numerical Example
4.1. The Application of Dual Hesitant Pythagorean Fuzzy TODIM Approach
4.2. Comparative Analysis
4.2.1. Comparison with the Dual Hesitant Pythagorean Fuzzy Weighted Average Operator
A1 = ({0.4982, 0.4925, 0.4884, 0.4826, 0.4878, 0.4819, 0.4777, 0.4716, |
0.4886, 0.4828, 0.4785, 0.4725, 0.4779, 0.4718, 0.4674, 0.4611}, |
{0.7012, 0.6936, 0.6849, 0.6774, 0.6908, 0.6833, 0.6747, 0.6673, |
0.6930, 0.6854, 0.6768, 0.6694, 0.6827, 0.6752, 0.6668, 0.6595, |
0.6832, 0.6757, 0.6672, 0.6600, 0.6730, 0.6657, 0.6573, 0.6502, |
0.6751, 0.6678, 0.6594, 0.6522, 0.6651, 0.6579, 0.6496, 0.6425, |
0.6962, 0.6886, 0.6800, 0.6725, 0.6858, 0.6784, 0.6699, 0.6626, |
0.6880, 0.6805, 0.6720, 0.6647, 0.6778, 0.6704, 0.6620, 0.6548, |
0.6783, 0.6709, 0.6625, 0.6552, 0.6682, 0.6609, 0.6526, 0.6455, |
0.6703, 0.6630, 0.6547, 0.6475, 0.6603, 0.6531, 0.6450, 0.6379}) |
A2 = ({0.5115, 0.5033, 0.4987, 0.4901, 0.5026, 0.4941, 0.4894, 0.4806, |
0.5037, 0.4952, 0.4906, 0.4817, 0.4945, 0.4858, 0.4810, 0.4718, |
0.5070, 0.4986, 0.4940, 0.4853, 0.4980, 0.4893, 0.4846, 0.4755, |
0.4990, 0.4904, 0.4857, 0.4767, 0.4897, 0.4809, 0.4760, 0.4667}, |
{0.6986, 0.6882, 0.6884, 0.6782, 0.6914, 0.6811, 0.6813, 0.6712, |
0.6916, 0.6814, 0.6816, 0.6714, 0.6845, 0.6743, 0.6745, 0.6645}) |
A3 = ({0.5303, 0.5201, 0.5216, 0.5110, 0.5220, 0.5115, 0.5130, 0.5021, |
0.5210, 0.5104, 0.5120, 0.5011, 0.5124, 0.5015, 0.5031, 0.4918, |
0.5244, 0.5139, 0.5154, 0.5046, 0.5159, 0.5051, 0.5066, 0.4955, |
0.5149, 0.5041, 0.5056, 0.4945, 0.5061, 0.4949, 0.4965, 0.4850}, |
{0.6213, 0.6154, 0.6042, 0.5985, 0.6102, 0.6044, 0.5934, 0.5878, |
0.6023, 0.5967, 0.5858, 0.5802, 0.5916, 0.5860, 0.5754, 0.5699}) |
A4 = ({0.5861, 0.5816, 0.5788, 0.5741, 0.5827, 0.5781, 0.5752, 0.5705, |
0.5832, 0.5786, 0.5757, 0.5710, 0.5797, 0.5750, 0.5721, 0.5674, |
0.5812, 0.5766, 0.5737, 0.5690, 0.5777, 0.5730, 0.5701, 0.5653, |
0.5782, 0.5735, 0.5706, 0.5658, 0.5746, 0.5699, 0.5670, 0.5621}, |
{0.5968, 0.5882, 0.5829, 0.5745, 0.5882, 0.5796, 0.5744, 0.5661, |
0.5685, 0.5602, 0.5552, 0.5472, 0.5602, 0.5521, 0.5472, 0.5392, |
0.5811, 0.5726, 0.5675, 0.5593, 0.5726, 0.5643, 0.5593, 0.5512, |
0.5535, 0.5454, 0.5406, 0.5327, 0.5454, 0.5375, 0.5327, 0.5250}) |
4.2.2. Comparison with the Dual Hesitant Pythagorean Fuzzy Weighted Geometric Operator
A1 = ({0.4553, 0.4487, 0.4487, 0.4422, 0.4337, 0.4274, 0.4274, 0.4212, |
0.4515, 0.4449, 0.4449, 0.4384, 0.4300, 0.4238, 0.4238, 0.4176}, |
{0.7117, 0.7060, 0.6993, 0.6934, 0.7071, 0.7014, 0.6945, 0.6884, |
0.7056, 0.6998, 0.6929, 0.6868, 0.7009, 0.6950, 0.6880, 0.6817, |
0.6980, 0.6920, 0.6849, 0.6785, 0.6932, 0.6870, 0.6798, 0.6733, |
0.6915, 0.6854, 0.6781, 0.6715, 0.6866, 0.6803, 0.6728, 0.6662, |
0.7080, 0.7023, 0.6954, 0.6894, 0.7034, 0.6975, 0.6906, 0.6844, |
0.7018, 0.6959, 0.6889, 0.6827, 0.6970, 0.6910, 0.6839, 0.6775, |
0.6941, 0.6880, 0.6808, 0.6743, 0.6892, 0.6829, 0.6756, 0.6690, |
0.6875, 0.6812, 0.6738, 0.6672, 0.6825, 0.6761, 0.6685, 0.6617}) |
A2 = ({0.4764, 0.4702, 0.4604, 0.4544, 0.4698, 0.4637, 0.4540, 0.4481, |
0.4392, 0.4335, 0.4244, 0.4190, 0.4331, 0.4275, 0.4185, 0.4131, |
0.4705, 0.4645, 0.4548, 0.4489, 0.4640, 0.4580, 0.4484, 0.4427, |
0.4338, 0.4282, 0.4192, 0.4138, 0.4278, 0.4223, 0.4134, 0.4081}, |
{0.7195, 0.7151, 0.7152, 0.7107, 0.7177, 0.7133, 0.7134, 0.7088, |
0.7165, 0.7121, 0.7122, 0.7076, 0.7147, 0.7102, 0.7103, 0.7058}) |
A3 = ({0.4924, 0.4874, 0.4852, 0.4803, 0.4856, 0.4807, 0.4785, 0.4737, |
0.4690, 0.4643, 0.4622, 0.4575, 0.4625, 0.4578, 0.4558, 0.4512, |
0.4875, 0.4826, 0.4804, 0.4755, 0.4807, 0.4759, 0.4737, 0.4690, |
0.4643, 0.4596, 0.4576, 0.4530, 0.4579, 0.4533, 0.4512, 0.4467}, |
{0.6531, 0.6420, 0.6423, 0.6307, 0.6491, 0.6378, 0.6381, 0.6263, |
0.6324, 0.6203, 0.6206, 0.6080, 0.6280, 0.6158, 0.6160, 0.6033}) |
A4 = ({0.5683, 0.5593, 0.5598, 0.5510, 0.5559, 0.5471, 0.5476, 0.5390, |
0.5624, 0.5535, 0.5540, 0.5453, 0.5501, 0.5415, 0.5420, 0.5334, |
0.5626, 0.5537, 0.5542, 0.5455, 0.5503, 0.5417, 0.5422, 0.5336, |
0.5568, 0.5480, 0.5485, 0.5399, 0.5446, 0.5361, 0.5366, 0.5281}, |
{0.6487, 0.6454, 0.6328, 0.6292, 0.6430, 0.6396, 0.6267, 0.6230, |
0.6426, 0.6392, 0.6263, 0.6226, 0.6367, 0.6332, 0.6200, 0.6163, |
0.6156, 0.6118, 0.5975, 0.5935, 0.6091, 0.6052, 0.5906, 0.5864, |
0.6087, 0.6048, 0.5901, 0.5860, 0.6020, 0.5981, 0.5830, 0.5788}) |
5. Concluding Remarks and Suggestions
Author Contributions
Funding
Conflicts of Interest
References
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({0.7,0.6},{0.7}) | ({0.4},{0.7,0.6}) | ({0.3},{0.8}) | ({0.4,0.3},{0.7,0.6}) | ({0.4},{0.7,0.6}) | |
({0.5,0.4},{0.6,0.5}) | ({0.5},{0.5,0.4}) | ({0.3,0.2},{0.8}) | ({0.5},{0.7}) | ({0.6,0.5},{0.7}) | |
({0.6,0.5},{0.5}) | ({0.5},{0.6}) | ({0.4},{0.7,0.6}) | ({0.4,0.3},{0.6}) | ({0.6,0.5},{0.8}) | |
({0.6,0.5},{0.5}) | ({0.5,0.4},{0.7}) | ({0.6},{0.8,0.7}) | ({0.7},{0.4,0.3}) | ({0.4,0.3},{0.7}) | |
({0.6,0.5},{0.6}) | ({0.5},{0.6,0.5}) | ({0.6},{0.7,0.6}) | ({0.5,0.4},{0.7}) | ({0.6},{0.7,0.6}) | |
({0.7},{0.6,0.5}) | ({0.5},{0.6,0.5}) | ({0.5,0.4},{0.8}) | ({0.5},{0.7}) | ({0.6,0.5},{0.7}) | |
({0.6,0.5},{0.5,0.4}) | ({0.7},{0.7}) | ({0.4},{0.6,0.5}) | ({0.7,0.6},{0.4}) | ({0.6},{0.8,0.7}) | |
({0.6},{0.6,0.5}) | ({0.6,0.5},{0.5}) | ({0.5},{0.7,0.6}) | ({0.6},{0.5,0.4}) | ({0.5,0.4},{0.6}) |
({0.7,0.6},{0.7,0.7}) | ({0.4,0.4},{0.7,0.6}) | ({0.3,0.3},{0.8,0.8}) | ({0.4,0.3},{0.7,0.6}) | ({0.4,0.4},{0.7,0.6}) | |
({0.5,0.4},{0.6,0.5}) | ({0.5,0.5},{0.5,0.4}) | ({0.3,0.2},{0.8,0.8}) | ({0.5,0.5},{0.7,0.7}) | ({0.6,0.5},{0.7,0.7}) | |
({0.6,0.5},{0.5,0.5}) | ({0.5,0.5},{0.6,0.6}) | ({0.4,0.4},{0.7,0.6}) | ({0.4,0.3},{0.6,0.6}) | ({0.6,0.5},{0.8,0.8}) | |
({0.6,0.5},{0.5,0.5}) | ({0.5,0.4},{0.7,0.7}) | ({0.6,0.6},{0.8,0.7}) | ({0.7,0.7},{0.4,0.3}) | ({0.4,0.3},{0.7,0.7}) | |
({0.6,0.5},{0.6,0.6}) | ({0.5,0.5},{0.6,0.5}) | ({0.6,0.6},{0.7,0.6}) | ({0.5,0.4},{0.7,0.7}) | ({0.6,0.6},{0.7,0.6}) | |
({0.7,0.7},{0.6,0.5}) | ({0.5,0.5},{0.6,0.5}) | ({0.5,0.4},{0.8,0.8}) | ({0.5,0.5},{0.7,0.7}) | ({0.6,0.5},{0.7,0.7}) | |
({0.6,0.5},{0.5,0.4}) | ({0.7,0.7},{0.7,0.7}) | ({0.4,0.4},{0.6,0.5}) | ({0.7,0.6},{0.4,0.4}) | ({0.6,0.6},{0.8,0.7}) | |
({0.6,0.6},{0.6,0.5}) | ({0.6,0.5},{0.5,0.5}) | ({0.5,0.5},{0.7,0.6}) | ({0.6,0.6},{0.5,0.4}) | ({0.5,0.4},{0.6,0.6}) |
Ordering | |
---|---|
Dual Hesitant Pythagoras Fuzzy TODIM | |
DHPFWA | |
DHPFWG |
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Share and Cite
Ji, X.; Yu, L.; Fu, J. Evaluating Personal Default Risk in P2P Lending Platform: Based on Dual Hesitant Pythagorean Fuzzy TODIM Approach. Mathematics 2020, 8, 8. https://doi.org/10.3390/math8010008
Ji X, Yu L, Fu J. Evaluating Personal Default Risk in P2P Lending Platform: Based on Dual Hesitant Pythagorean Fuzzy TODIM Approach. Mathematics. 2020; 8(1):8. https://doi.org/10.3390/math8010008
Chicago/Turabian StyleJi, Xiaonan, Lixia Yu, and Jiapei Fu. 2020. "Evaluating Personal Default Risk in P2P Lending Platform: Based on Dual Hesitant Pythagorean Fuzzy TODIM Approach" Mathematics 8, no. 1: 8. https://doi.org/10.3390/math8010008