Table 5.
Mathematical operators’ analysis in the context of COVID-19
| Studies | Layer | Operator | Integrated in MCDM method | Originality of the operator | Numerical environment | Type of operator | |||
|---|---|---|---|---|---|---|---|---|---|
| Existing | New Proposed | Crisp | Fuzzy | Differences/similarity | Aggregation | ||||
| Pamučar et al. (2020) | Evaluation | Bonferroni integration operator | RAFSI | ✓ | – | – | ✓ | – | ✓ |
| Samanıloğlu and Kaya (2020) | Ordered weighting averaging | AHP | ✓ | – | – | ✓ | – | ✓ | |
| Ocampo and Yamagishi (2020) | Crispification operator | DEMATEL | ✓ | – | – | ✓ | – | ✓ | |
| Yang et al. (2020) | 1. Spherical normal fuzzy Bonferroni mean (SpNoFBM) operator | – | – | ✓ | – | ✓ | – | ✓ | |
| 2. Spherical normal fuzzy weighted Bonferroni mean (SpNoFGBM) operator | |||||||||
| Mahanta and Panda (2020) | Distance and similarity measures | – | ✓ | – | – | ✓ | ✓ | – | |
| Abdel-Basst et al. (2020b) | Plithogenic aggregation operator | BWM-TOPSIS | ✓ | – | – | ✓ | – | ✓ | |
| Garg et al. (2020) | 1. Fermatean fuzzy Yager weighted average (FFYWA) | – | – | – | – | ||||
| 2. Fermatean fuzzy Yager ordered weighted average (FFYOWA) | |||||||||
| 3. Fermatean fuzzy Yager hybrid weighted average (FFYHWA) | |||||||||
| 4. Fermatean fuzzy Yager weighted geometric (FFYWG) | |||||||||
| 5. Fermatean fuzzy Yager ordered weighted geometric (FFYOWG) | |||||||||
| 6. Fermatean fuzzy Yager hybrid weighted geometric (FFYHWG) | |||||||||
| Yang et al. (2021) | 1. Complex q-rung orthopair uncertain linguistic partitioned Bonferroni mean (CQROULPBM) operator | – | – | ✓ | – | ✓ | – | ✓ | |
| 2. Complex q–rung orthopair uncertain linguistic weighted partitioned Bonferroni mean (CQROULWPBM) operator | |||||||||
| Naeem et al. (2020) | Euclidian distance | PmF-TOPSIS | ✓ | – | – | ✓ | ✓ | – | |
| Ortiz–Barrios et al. (2020) | Algebraic operators | AHP-DEMATEL | ✓ | – | – | ✓ | – | ✓ | |
| Wan et al. (2021) | Arithmetic operations | BWM-VIKOR | ✓ | – | – | ✓ | – | ✓ | |
| Zhang et al. (2020) | Weighted arithmetic aggregation operator | MULTIMOORA | ✓ | – | – | ✓ | – | ✓ | |
| Mishra et al. (2019) | HF-weighted average (HFWA) operator | ARAS | ✓ | – | – | ✓ | – | ✓ | |
| Ashraf and Abdullah (2020) |
1. Einstein norm‐based aggregation operators: 2. Spherical fuzzy Einstein weighted average |
TOPSIS-GRA | – | ✓ | – | ✓ | – | ✓ | |
| 3. Spherical fuzzy Einstein weighted geometric | |||||||||
| 4. Spherical fuzzy Einstein order weighted average | |||||||||
| 5. Spherical fuzzy Einstein order weighted geometric aggregation | |||||||||
| Sharma et al. (2020) | Fuzzy linguistic quantifier ordered weighted aggregation (FLQOWA) operator | FLQOWA | ✓ | – | – | ✓ | – | ✓ | |
| Ecer and Pamucar (2021) | 1. Intuitionistic fuzzy weighted averaging (IFWA) operator | MARCOS | ✓ | – | – | ✓ | – | ✓ | |
| 2. Max and min operators | ✓ | – | |||||||
| Mardani et al. (2020) | 3. Hesitant fuzzy weighted averaging (HFWA) | SWARA–WASPAS | ✓ | – | – | ✓ | – | ✓ | |
| 4. Hesitant fuzzy weighted geometric (HFWG) | |||||||||
| Gong et al. (2021) | Linguistic hesitant fuzzy weighted averaging (LHFWA) operator | BWM- TODIM | ✓ | – | – | ✓ | – | ✓ | |
| Percentages | 77.77 | 22.22 | 0 | 100 | 16.66 | 88.88 | |||
| Ashraf et al. (2020) | Development | 1. Spherical fuzzy weighted averaging (SFWA) operator | – | ✓ | – | – | ✓ | – | ✓ |
| 2. Spherical fuzzy weighted geometric (SFWG) operator | – | ✓ | |||||||
| 3. Euclidian distance | ✓ | – | |||||||
| Albahri (2020) | Euclidian distance | SODOSM | ✓ | – | ✓ | – | ✓ | – | |
| Alsalem et al. (2021) | Arithmetic mean | AHP–VIKOR | ✓ | – | ✓ | – | – | ✓ | |
| Zidan (2021) | Arithmetic mean | PFDOSM | ✓ | – | – | ✓ | – | ✓ | |
| Zaidan (2021a) | Arithmetic mean | T-SFDOSM | ✓ | – | – | ✓ | – | ✓ | |
| Zaidan (2021b) | 1. q–rung orthopair fuzzy arithmetic mean (q-ROFA) | q-ROFWZIC | ✓ | – | – | ✓ | – | ✓ | |
| 2. q-rung orthopair fuzzy weighted arithmetic mean (q-ROFWA) aggregation | q-ROFDOSM | ||||||||
| Percentages | 100 | 0 | 33.33 | 66.66 | 33.33 | 100 | |||
N/A = Not applicable
(✓) = Including
(–) = Not including