A Novel Early Warning Method for Handling Non-Homogeneous Information
Abstract
:1. Introduction
2. Preliminary Knowledge
2.1. Linguistic Terms
2.2. Hesitant Fuzzy Linguistic Term Sets
2.3. Fuzzy TOPSIS Method Based on Alpha-Level Sets
2.4. Related Work
3. Proposed Method
3.1. Problem Definition
3.2. Information Collection
3.3. Information Transformation
3.4. Information Aggregation
3.5. Fuzzy TOPSIS Method Based on Alpha-Level Sets
- Step 1: To judge the intersection relation between and .
- Step 2: When , if , then the status results of belongs to the corresponding status ; if , then the status results of belongs to the corresponding status ; and if there exists and , then the status results of belongs to the corresponding status .
4. Illustrative Example and Comparison
4.1. Illustrative Example
4.1.1. Problem Definition
4.1.2. Information Collection
4.1.3. Information Transformation
4.1.4. Information Aggregation
4.1.5. Fuzzy TOPSIS Method Based on Alpha-Level Sets
4.1.6. Sensitivity Analysis
4.2. Comparisons with Existing Studies
5. Discussion
6. Conclusions and Future Work
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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S | Linguistic Terms | Fuzzy Numbers |
---|---|---|
very poor (VP) | ||
poor (P) | ||
medium (M) | ||
good (G) | ||
very good (VG) |
Status () | Very Dangerous () | Dangerous () | Fairly Dangerous () | Fairly Safety () | Safety () |
---|---|---|---|---|---|
[0, 0.2) | [0.2, 0.4) | [0.4, 0.6) | [0.6, 0.8) | [0.8, 1] |
Criteria | Description | Information Type |
---|---|---|
Rainfall (mm) | The higher the rainfall, the more easily a landslide occurs | I |
Coverage rate of the forest (%) | The lower the coverage rate of the forest, the more easily a landslide occurs | N |
Saturated water content of soil (%) | The higher the saturated water content of the soil, the more easily a landslide occurs | N |
Slope (◦) | The higher the slope, the more easily a landslide occurs | N |
Influence Degree of Earthquake | The higher the influence degree of an earthquake, the more easily a landslide occurs | |
Degree of human activity | The higher the degree of human activity, the more easily a landslide occurs | |
Stability of Geological Structure | The lower the stability of a geological structure, the more easily a landslide occurs |
Experts | Objects | Criteria | ||||||
---|---|---|---|---|---|---|---|---|
[35,55] | 62 | 33 | 35 | M | L | H | ||
[25,38] | 45 | 26 | 29 | L | L | M | ||
[20,35] | 33 | 40 | 38 | VL | H | H | ||
[30,46] | 65 | 38 | 40 | H | H | M | ||
[18,35] | 55 | 29 | 33 | M | bt M and FH | M | ||
[23,34] | 42 | 35 | 28 | L | M | H | ||
[40,50] | 58 | 35 | 33 | bt L and M | M | FH | ||
[22,35] | 50 | 28 | 36 | M | FH | M | ||
[25,40] | 44 | 38 | 32 | L | L | M | ||
[20,38] | 53 | 44 | 37 | M | H | bt M and FH | ||
[22,38] | 48 | 36 | 31 | H | bt FH and H | H | ||
[21,44] | 39 | 29 | 30 | At most H | M | H | ||
[33,45] | 66 | 29 | 38 | L | L | M | ||
[18,36] | 53 | 33 | 41 | FH | L | L | ||
[18,24] | 48 | 42 | 26 | M | M | FH | ||
[23,38] | 50 | 41 | 33 | L | At most H | M | ||
[16,24] | 49 | 39 | 29 | H | FH | FH | ||
[20,34] | 45 | 34 | 34 | H | L | FH |
Experts | Criteria Importance | ||||||
---|---|---|---|---|---|---|---|
VHI | HI | bt MI and HI | HI | MI | LI | HI | |
At least HI | HI | MI | VHI | LI | VLI | MI | |
VHI | MI | HI | bt HI and VHI | LI | LI | VHI |
Experts | Objects | Criteria | |||
---|---|---|---|---|---|
(0.4872,0.4872,1.0000,1.0000) | (0.9394,0.9394,0.9394,0.9394) | (0.7500,0.7500,0.7500,0.7500) | (0.8537,0.8537,0.8537,0.8537) | ||
(0.2308,0.2308,0.5641,0.5641) | (0.6818,0.6818,0.6818,0.6818) | (0.5909,0.5909,0.5909,0.5909) | (0.7073,0.7073,0.7073,0.7073) | ||
(0.1026,0.1026,0.4872,0.4872) | (0.5000,0.5000,0.5000,0.5000) | (0.9091,0.9091,0.9091,0.9091) | (0.9268,0.9268,0.9268,0.9268) | ||
(0.3590,0.3590,0.7692,0.7692) | (0.9848,0.9848,0.9848,0.9848) | (0.8636,0.8636,0.8636,0.8636) | (0.9756,0.9756,0.9756,0.9756) | ||
(0.0513,0.0513,0.4872,0.4872) | (0.8333,0.8333,0.8333,0.8333) | (0.6591,0.6591,0.6591,0.6591) | (0.8049,0.8049,0.8049,0.8049) | ||
(0.1795,0.1795,0.4615,0.4615) | (0.6364,0.6364,0.6364,0.6364) | (0.7955,0.7955,0.7955,0.7955) | (0.6829,0.6829,0.6829,0.6829) | ||
(0.6154,0.6154,0.8718,0.8718) | (0.8788,0.8788,0.8788,0.8788) | (0.7955,0.7955,0.7955,0.7955) | (0.8049,0.8049,0.8049,0.8049) | ||
(0.1538,0.1538,0.4872,0.4872) | (0.7576,0.7576,0.7576,0.7576) | (0.6364,0.6364,0.6364,0.6364) | (0.8780,0.8780,0.8780,0.8780) | ||
(0.2308,0.2308,0.6154,0.6154) | (0.6667,0.6667,0.6667,0.6667) | (0.8636,0.8636,0.8636,0.8636) | (0.7805,0.7805,0.7805,0.7805) | ||
(0.1026,0.1026,0.5641,0.5641) | (0.8030,0.8030,0.8030,0.8030) | (1.0000,1.0000,1.0000,1.0000) | (1.9024,0.9024,0.9024,0.9024) | ||
(0.1538,0.1538,0.5641,0.5641) | (0.7273,0.7273,0.7273,0.7273) | (0.8182,0.8182,0.8182,0.8182) | (0.7561,0.7561,0.7561,0.7561) | ||
(0.1282,0.1282,0.7179,0.7179) | (0.5909,0.5909,0.5909,0.5909) | (0.6591,0.6591,0.6591,0.6591) | (0.7317,0.7317,0.7317,0.7317) | ||
(0.4359,0.4359,0.7436,0.7436) | (1.0000,1.0000,1.0000,1.0000) | (0.6591,0.6591,0.6591,0.6591) | (0.9268,0.9268,0.9268,0.9268) | ||
(0.0513,0.0513,0.5128,0.5128) | (0.8030,0.8030,0.8030,0.8030) | (0.7500,0.7500,0.7500,0.7500) | (0.0000,1.0000,1.0000,1.0000) | ||
(0.0513,0.0513,0.2051,0.2051) | (0.7273,0.7273,0.7273,0.7273) | (0.9545,0.9545,0.9545,0.9545) | (0.6341,0.6341,0.6341,0.6341) | ||
(0.1795,0.1795,0.5641,0.5641) | (0.7576,0.7576,0.7576,0.7576) | (0.9318,0.9318,0.9318,0.9318) | (0.8049,0.8049,0.8049,0.8049) | ||
(0.0000,0.0000,0.2051,0.2051) | (0.7424,0.7424,0.7424,0.7424) | (0.8864,0.8864,0.8864,0.8864) | (0.7073,0.7073,0.7073,0.7073) | ||
(0.1026,0.1026,0.4615,0.4615) | (0.6818,0.6818,0.6818,0.6818) | (0.7727,0.7727,0.7727,0.7727) | (0.8293,0.8293,0.8293,0.8293) |
Experts | Objects | Criteria | ||
---|---|---|---|---|
(0.3300,0.5000,0.5000,0.6700) | (0.1700,0.3300,0.3300,0.5000) | (0.6700,0.8300,0.8300,1.0000) | ||
(0.1700,0.3300,0.3300,0.5000) | (0.1700,0.3300,0.3300,0.5000) | (0.3300,0.5000,0.5000,0.6700) | ||
(0.0000,0.1700,0.1700,0.3300) | (0.6700,0.8300,0.8300,1.0000) | (0.6700,0.8300,0.8300,1.0000) | ||
(0.6700,0.8300,0.8300,1.0000) | (0.6700,0.8300,0.8300,1.0000) | (0.3300,0.5000,0.5000,0.6700) | ||
(0.3300,0.5000,0.5000,0.6700) | (0.3400,0.5000,0.6700,0.8400) | (0.3300,0.5000,0.5000,0.6700) | ||
(0.1700,0.3300,0.3300,0.5000) | (0.3300,0.5000,0.5000,0.6700) | (0.6700,0.8300,0.8300,1.0000) | ||
(0.1700,0.3400,0.5000,0.6700) | (0.3300,0.5000,0.5000,0.6700) | (0.5000,0.6700,0.6700,0.8300) | ||
(0.3300,0.5000,0.5000,0.6700) | (0.5000,0.6700,0.6700,0.8300) | (0.3300,0.5000,0.5000,0.6700) | ||
(0.1700,0.3300,0.3300,0.5000) | (0.1700,0.3300,0.3300,0.5000) | (0.3300,0.5000,0.5000,0.6700) | ||
(0.3300,0.5000,0.5000,0.6700) | (0.6700,0.8300,0.8300,1.0000) | (0.3400,0.5000,0.6700,0.8400) | ||
(0.6700,0.8300,0.8300,1.0000) | (0.5000,0.6700,0.8300,1.0000) | (0.6700,0.8300,0.8300,1.0000) | ||
(0.0000,0.0000,0.5900,0.8400) | (0.3300,0.5000,0.5000,0.6700) | (0.6700,0.8300,0.8300,1.0000) | ||
(0.1700,0.3300,0.3300,0.5000) | (0.1700,0.3300,0.3300,0.5000) | (0.3300,0.5000,0.5000,0.6700) | ||
(0.5000,0.6700,0.6700,0.8300) | (0.5000,0.6700,0.6700,0.8300) | (0.1700,0.3300,0.3300,0.5000) | ||
(0.3300,0.5000,0.5000,0.6700) | (0.3300,0.5000,0.5000,0.6700) | (0.5000,0.6700,0.6700,0.8300) | ||
(0.1700,0.3300,0.3300,0.5000) | (0.0000,0.0000,0.5900,0.8400) | (0.3300,0.5000,0.5000,0.6700) | ||
(0.6700,0.8300,0.8300,1.0000) | (0.5000,0.6700,0.6700,0.8300) | (0.5000,0.6700,0.6700,0.8300) | ||
(0.6700,0.8300,0.8300,1.0000) | (0.1700,0.3300,0.3300,0.5000) | (0.5000,0.6700,0.6700,0.8300) |
Experts | Transformed Criteria Importance | |||
---|---|---|---|---|
(0.6700,0.8300,0.8300,1.0000) | (0.5000,0.6700,0.6700,0.8300) | (0.3400,0.5000,0.6700,0.8400) | (0.5000,0.6700,0.6700,0.8300) | |
(0.5000,0.8600,0.8600,1.0000) | (0.5000,0.6700,0.6700,0.8300) | (0.3300,0.5000,0.5000,0.6700) | (0.6700,0.8300,0.8300,1.0000) | |
(0.6700,0.8300,0.8300,1.0000) | (0.3300,0.5000,0.5000,0.6700) | (0.5000,0.3300,0.6700,0.8300) | (0.5000,0.6700,0.8300,1.0000) |
Experts | Transformed Criteria Importance | ||
---|---|---|---|
(0.3300,0.5000,0.5000,0.6700) | (0.1700,0.3300,0.3300,0.5000) | (0.5000,0.6700,0.6700,0.8300) | |
(0.1700,0.3300,0.3300,0.5000) | (0.0000,0.1700,0.1700,0.6700) | (0.3300,0.5000,0.5000,0.6700) | |
(0.1700,0.3300,0.3300,0.5000) | (0.1700,0.3300,0.3300,0.5000) | (0.6700,0.8300,0.8300,1.0000) |
Aggregated Information | Criteria | |||
---|---|---|---|---|
X | (0.4359,0.5128,0.8718,1.0000) | (0.8788,0.9394,0.9394,1.0000) | (0.6591,0.7348,0.7348,0.7955) | (0.8049,0.8618,0.8618,0.9268) |
(0.0513,0.1453,0.5214,0.5641) | (0.6818,0.7475,0.7475,0.8030) | (0.5909,0.6591,0.6591,0.7500) | (0.7073,0.8618,0.8618,1.0000) | |
(0.0513,0.1282,0.4359,0.6154) | (0.5000,0.6313,0.6313,0.7273) | (0.8636,0.9091,0.9091,0.9545) | (0.6341,0.7805,0.7805,0.9268) | |
(0.1026,0.2137,0.6325,0.7692) | (0.7576,0.8485,0.8485,0.9848) | (0.8636,0.9318,0.9318,1.0000) | (0.8049,0.8943,0.8943,0.9756) | |
(0.0000,0.0684,0.4188,0.5641) | (0.7273,0.7677,0.7677,0.8333) | (0.6591,0.7879,0.7879,0.8864) | (0.7073,0.7561,0.7561,0.8049) | |
(0.1026,0.1368,0.5470,0.7179) | (0.5909,0.6364,0.6364,0.6818) | (0.6591,0.7424,0.7424,0.7955) | (0.6829,0.7480,0.7480,0.8293) | |
W | (0.5000,0.8400,0.8400,1.0000) | (0.3300,0.6133,0.6133,0.8300) | (0.3300,0.5567,0.6133,0.8400) | (0.5000,0.7233,0.7767,1.0000) |
Aggregated Information | Criteria | ||
---|---|---|---|
X | (0.1700,0.3900,0.4433,0.6700) | (0.1700,0.3867,0.3867,0.6700) | (0.3300,0.6667,0.6667,1.0000) |
(0.1700,0.5000,0.5000,0.8300) | (0.1700,0.4433,0.4433,0.8300) | (0.1700,0.4433,0.4433,0.6700) | |
(0.0000,0.3333,0.3333,0.6700) | (0.1700,0.5533,0.5533,1.0000) | (0.3300,0.6667,0.6667,1.0000) | |
(0.1700,0.5533,0.5533,1.0000) | (0.0000,0.5533,0.7500,1.0000) | (0.3300,0.5000,0.5567,0.8400) | |
(0.3300,0.7200,0.7200,1.0000) | (0.3400,0.6133,0.7233,1.0000) | (0.3300,0.6667,0.6667,1.0000) | |
(0.0000,0.3867,0.5833,1.0000) | (0.1700,0.4433,0.4433,0.6700) | (0.5000,0.7767,0.7767,1.0000) | |
W | (0.1700,0.3867,0.3867,0.6700) | (0.0000,0.2767,0.2767,0.5000) | (0.3300,0.6667,0.6667,1.0000) |
Alpha | ||||||
---|---|---|---|---|---|---|
Status | Status | Status | ||||
0 | [0.4027,0.9478] | FD | [0.2613,0.8143] | D | [0.2732,0.8792] | D |
0.1 | [0.4348,0.9357] | FD | [0.2879,0.7930] | D | [0.2989,0.8589] | D |
0.2 | [0.4634,0.9190] | FD | [0.3146,0.7760] | D | [0.3253,0.8357] | D |
0.3 | [0.4903,0.9012] | FD | [0.3412,0.7586] | D | [0.3519,0.8106] | D |
0.4 | [0.5169,0.8857] | FD | [0.3675,0.7403] | D | [0.3786,0.7845] | D |
0.5 | [0.5431,0.8685] | FD | [0.3936,0.7212] | D | [0.4053,0.7578] | FD |
0.6 | [0.5688,0.8495] | FD | [0.4192,0.7014] | FD | [0.4317,0.7307] | FD |
0.7 | [0.5939,0.8291] | FD | [0.4443,0.6814] | FD | [0.4577,0.7040] | FD |
0.8 | [0.6182,0.8074] | FS | [0.4688,0.6611] | FD | [0.4834,0.6772] | FD |
0.9 | [0.6416,0.7845] | FS | [0.4925,0.6400] | FD | [0.5085,0.6501] | FD |
1 | [0.6647,0.7600] | FS | [0.5160,0.6182] | FD | [0.5332,0.6231] | FD |
0.7012 | FS | 0.5551 | FD | 0.5800 | FD |
Alpha | ||||||
---|---|---|---|---|---|---|
Status | Status | Status | ||||
0 | [0.3280,0.9328] | D | [0.3202,0.8591] | D | [0.2880,0.8686] | D |
0.1 | [0.3544,0.9176] | D | [0.3409,0.8404] | D | [0.3126,0.8495] | D |
0.2 | [0.3808,0.8992] | D | [0.3619,0.8193] | D | [0.3378,0.8277] | D |
0.3 | [0.4073,0.8802] | FD | [0.3832,0.7984] | D | [0.3632,0.8046] | D |
0.4 | [0.4337,0.8609] | FD | [0.4049,0.7775] | FD | [0.3886,0.7837] | D |
0.5 | [0.4599,0.8405] | FD | [0.4267,0.7567] | FD | [0.4137,0.7630] | FD |
0.6 | [0.4855,0.8188] | FD | [0.4488,0.7350] | FD | [0.4384,0.7428] | FD |
0.7 | [0.5106,0.7961] | FD | [0.4711,0.7128] | FD | [0.4625,0.7229] | FD |
0.8 | [0.5349,0.7724] | FD | [0.4935,0.6902] | FD | [0.4860,0.7025] | FD |
0.9 | [0.5584,0.7478] | FD | [0.5159,0.6672] | FD | [0.5087,0.6815] | FD |
1 | [0.5811,0.7225] | FD | [0.5384,0.6441] | FD | [0.5306,0.6600] | FD |
0.6465 | FS | 0.5912 | FD | 0.5880 | FD |
Alpha | ||||||
---|---|---|---|---|---|---|
Status | Status | Status | ||||
0 | [0.3696,0.9093] | D | [0.2512,0.8169] | D | [0.2453,0.8606] | D |
0.1 | [0.3992,0.8952] | D | [0.2781,0.7936] | D | [0.2696,0.8376] | D |
0.2 | [0.4282,0.8783] | FD | [0.3053,0.7749] | D | [0.295,0.812] | D |
0.3 | [0.4564,0.8595] | FD | [0.3324,0.7557] | D | [0.3213,0.7847] | D |
0.4 | [0.4817,0.8395] | FD | [0.3594,0.7355] | D | [0.3481,0.7565] | D |
0.5 | [0.5065,0.8186] | FD | [0.3863,0.7145] | D | [0.3752,0.7276] | D |
0.6 | [0.5307,0.797] | FD | [0.4128,0.693] | FD | [0.4024,0.6985] | FD |
0.7 | [0.5539,0.7756] | FD | [0.4389,0.6714] | FD | [0.4294,0.6693] | FD |
0.8 | [0.577,0.7535] | FD | [0.4645,0.649] | FD | [0.4563,0.6405] | FD |
0.9 | [0.6001,0.7309] | FD | [0.4894,0.6259] | FD | [0.4831,0.6119] | FD |
1 | [0.6238,0.7074] | FD | [0.5143,0.6021] | FD | [0.5097,0.5828] | FD |
0.6587 | FS | 0.5484 | FD | 0.5508 | FD |
Alpha | ||||||
---|---|---|---|---|---|---|
Status | Status | Status | ||||
0 | [0.3075,0.9376] | D | [0.3211,0.8704] | D | [0.2571,0.8827] | D |
0.1 | [0.3364,0.9217] | D | [0.3434,0.8530] | D | [0.2807,0.8640] | D |
0.2 | [0.3655,0.9006] | D | [0.3663,0.8326] | D | [0.3057,0.8411] | D |
0.3 | [0.3929,0.8789] | D | [0.3896,0.8106] | D | [0.3315,0.816] | D |
0.4 | [0.4205,0.8569] | FD | [0.4133,0.7889] | FD | [0.3579,0.7908] | D |
0.5 | [0.4479,0.8333] | FD | [0.4372,0.7676] | FD | [0.3845,0.7669] | D |
0.6 | [0.4750,0.8082] | FD | [0.4614,0.7458] | FD | [0.4110,0.7438] | FD |
0.7 | [0.5017,0.7819] | FD | [0.4857,0.7234] | FD | [0.4373,0.7211] | FD |
0.8 | [0.5279,0.7546] | FD | [0.5099,0.7005] | FD | [0.4632,0.6979] | FD |
0.9 | [0.5533,0.7264] | FD | [0.5342,0.6772] | FD | [0.4885,0.6738] | FD |
1 | [0.5779,0.6975] | FD | [0.5583,0.6536] | FD | [0.5132,0.6490] | FD |
0.6366 | FS | 0.602 | FS | 0.5763 | FD |
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Zhang, Z.-X.; Wang, L.; Wang, Y.-M. A Novel Early Warning Method for Handling Non-Homogeneous Information. Mathematics 2022, 10, 3016. https://doi.org/10.3390/math10163016
Zhang Z-X, Wang L, Wang Y-M. A Novel Early Warning Method for Handling Non-Homogeneous Information. Mathematics. 2022; 10(16):3016. https://doi.org/10.3390/math10163016
Chicago/Turabian StyleZhang, Zi-Xin, Liang Wang, and Ying-Ming Wang. 2022. "A Novel Early Warning Method for Handling Non-Homogeneous Information" Mathematics 10, no. 16: 3016. https://doi.org/10.3390/math10163016
APA StyleZhang, Z. -X., Wang, L., & Wang, Y. -M. (2022). A Novel Early Warning Method for Handling Non-Homogeneous Information. Mathematics, 10(16), 3016. https://doi.org/10.3390/math10163016