Table 5 Lower approximation for roughly fuzzy hypersoft definable

\(\hat{\zeta }_1\)

\(\hat{\Upsilon }(\hat{v}_1)\), \(\hat{\Upsilon }(\hat{v}_5)\), \(\hat{\Upsilon }(\hat{v}_6)\), \(\hat{\Upsilon }(\hat{v}_9)\), \(\hat{\Upsilon }(\hat{v}_{11})\)

\(\hat{\Psi }(\hat{v}_5) \subseteq \hat{M}\)

partially Yes

\(\hat{\zeta }_2\)

\(\hat{\Upsilon }(\hat{v}_3)\), \(\hat{\Upsilon }(\hat{v}_5)\), \(\hat{\Upsilon }(\hat{v}_9)\)

\(\hat{\Upsilon }(\hat{v}_3) \subseteq \hat{M}\)

partially Yes

\(\hat{\zeta }_3\)

\(\hat{\Upsilon }(\hat{v}_1)\), \(\hat{\Upsilon }(\hat{v}_{11})\), \(\hat{\Upsilon }(\hat{v}_{14})\)

\(\hat{\Upsilon }(\hat{v}_1) \nsubseteq \hat{M}\)

No

\(\hat{\zeta }_4\)

\(\hat{\Upsilon }(\hat{v}_3)\), \(\hat{\Upsilon }(\hat{v}_6)\), \(\hat{\Upsilon }(\hat{v}_9)\), \(\hat{\Upsilon }(\hat{v}_{11})\), \(\hat{\Upsilon }(\hat{v}_{14})\)

\(\hat{\Upsilon }(\hat{v}_{14}) \nsubseteq \hat{M}\)

No

\(\hat{\zeta }_5\)

\(\hat{\Upsilon }(\hat{v}_1)\), \(\hat{\Upsilon }(\hat{v}_{5})\), \(\hat{\Upsilon }(\hat{v}_{9})\), \(\hat{\Upsilon }(\hat{v}_{14})\)

\(\hat{\Upsilon }(\hat{v}_5) \subseteq \hat{M}\)

partially Yes

\(\hat{\zeta }_6\)

\(\hat{\Upsilon }(\hat{v}_3)\), \(\hat{\Upsilon }(\hat{v}_{5})\), \(\hat{\Upsilon }(\hat{v}_{14})\)

\(\hat{\Upsilon }(\hat{v}_5) \subseteq \hat{M}\)

partially Yes

\(\hat{\zeta }_7\)

\(\hat{\Upsilon }(\hat{v}_1)\), \(\hat{\Upsilon }(\hat{v}_6)\), \(\hat{\Upsilon }(\hat{v}_9)\), \(\hat{\Upsilon }(\hat{v}_{11})\)

\(\hat{\Upsilon }(\hat{v}_6) \nsubseteq \hat{M}\)

No

\(\hat{\zeta }_8\)

\(\hat{\Upsilon }(\hat{v}_1)\), \(\hat{\Upsilon }(\hat{v}_6)\), \(\hat{\Upsilon }(\hat{v}_9)\), \(\hat{\Upsilon }(\hat{v}_{11})\) , \(\hat{\Upsilon }(\hat{v}_{14})\)

\(\hat{\Upsilon }(\hat{v}_{14}) \nsubseteq \hat{M}\)

No