Table 12 Overall results for comparative analysis.

CFS⁴⁰

Cannot discuss CPyFR data

No result

No solution

CIFS⁴¹

Cannot discuss CPyFR data

No result

No solution

CPyFS⁴²

Cannot discuss CPyFR data

No result

No solution

FRS³¹

Cannot discuss CPyFR data

No result

No solution

IFRS³²

Cannot discuss CPyFR data

No result

No solution

Multi-granulation PyFRS³³

Cannot discuss CPyFR data

No result

No solution

The WASPAS Method based on IFS⁴³

Cannot discuss CPyFR data

No result

No solution

The WASPAS techniques for PyF data⁴⁴

Cannot discuss CPyFR data

No result

No solution

Complex intuitionistic fuzzy rough⁴⁵ approach

Cannot discuss CPyFR data

No result

No solution

Hesitant FS^13,14 approaches

Cannot discuss CPyFR data

No result

No solution

The WASPAS method based on the proposed theory

\(\:S\left({\text{B}}_{1}\right)=0.47488,\:\)

\(\:S\left({\text{B}}_{2}\right)=0.43453\)

\(\:S\left({\text{B}}_{3}\right)=0.44099,\)

\(\:\:S\left({\text{B}}_{4}\right)=0.46946\)

\(\:{A}_{L1}>{A}_{L4}>{A}_{L3}>{A}_{L2}\)

\(\:{A}_{L1}\)

CPyFRYWA AOs (proposed)

\(\:S\left({\text{B}}_{1}\right)=0.5662,\)

\(\:\:S\left({\text{B}}_{2}\right)=0.5082\)

\(\:S\left({\text{B}}_{3}\right)=0.5165,\:\)

\(\:S\left({\text{B}}_{4}\right)=0.5537\)

\(\:{A}_{L1}>{A}_{L4}>{A}_{L3}>{A}_{L2}\)

\(\:{A}_{L1}\)

CPyFRYWG AOs (proposed)

\(\:S\left({\text{B}}_{1}\right)=0.5308,\)

\(\:\:S\left({\text{B}}_{2}\right)=0.4930\)

\(\:S\left({\text{B}}_{3}\right)=0.50027,\)

\(\:\:S\left({\text{B}}_{4}\right)=0.5269\)

\(\:{A}_{L1}>{A}_{L4}>{A}_{L3}>{A}_{L2}\)

\(\:{A}_{L1}\)