Table 12 Overall results.

XU and Yager³¹

Impossible

Impossible

Mahmood et al.³² approach

Impossible

Impossible

Ye³³ approach

Impossible

Impossible

Tan³⁷

Impossible

Impossible

Wei and Lu³⁸

Impossible

Impossible

Arora and Garg’s³⁹ method

Impossible

Impossible

Zulqarnain et al.⁴⁰ method

Impossible

Impossible

Jana et al.⁴¹ method

Impossible

Impossible

IVBPFSWA operators (Proposed)

\(\:Sc\left({{\rm\:Y}}_{1}\right)=0.5204,\)

\(\:\:Sc\left({{\rm\:Y}}_{2}\right)=0.5182\)

\(\:Sc\left({{\rm\:Y}}_{3}\right)=0.5053,\)

\(\:\:Sc\left({{\rm\:Y}}_{4}\right)=0.5441\:\)

\(\:Sc\left({{\rm\:Y}}_{4}\right)>Sc\left({{\rm\:Y}}_{1}\right)>Sc\left({{\rm\:Y}}_{2}\right)>Sc\left({{\rm\:Y}}_{3}\right)\)

IVBPFSWGA operators (Proposed)

\(\:Sc\left({{\rm\:Y}}_{1}\right)=0.4951,\)

\(\:\:Sc\left({{\rm\:Y}}_{2}\right)=0.4898\)

\(\:Sc\left({{\rm\:Y}}_{3}\right)=0.4838,\)

\(\:\:Sc\left({{\rm\:Y}}_{4}\right)=0.5125\:\)

\(\:Sc\left({{\rm\:Y}}_{4}\right)>Sc\left({{\rm\:Y}}_{1}\right)>Sc\left({{\rm\:Y}}_{2}\right)>Sc\left({{\rm\:Y}}_{3}\right)\)