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| Theories | Merits | Limitations |
|---|---|---|
| Fuzzy sets (Zadeh, 1965) | Allocate MSD in [0, 1] | Can not allocate NMSD |
| IFSs (Atanassov, 1986) | Allocate both MSD and NMSD, | Fails when MSD+NMSD > 1 |
| PyFSs (Yager, 2014) | Allocate both MSD and NMSD, | Fails when MSD2 + NMSD2 > 1 |
| superior than the IFNs | ||
| q-ROPFSs (Yager, 2017) | Allocate both MSD and NMSD, | Can not deal with MSDq + NMSDq > 1 |
| superior than IFNs, PFNs, | and MSD = NMSD = 1 | |
| a broader space for MSD and NMSD & |
