Table 6 Score value and corresponding ranking of alternatives under both existing and newly proposed methods.

LIFOWA¹⁷

\(\:{u}_{1.0312}\)

\(\:{u}_{0.6087}\)

\(\:{u}_{0.5731}\)

\(\:{u}_{0.7587}\)

\(\:{\chi\:}_{1}>{\chi\:}_{4}>{\chi\:}_{2}>{\chi\:}_{3}\)

LIFOWG¹⁷

\(\:{u}_{0.9568}\)

\(\:{u}_{0.5438}\)

\(\:{u}_{0.5403}\)

\(\:{u}_{0.7304}\)

\(\:{\chi\:}_{1}>{\chi\:}_{4}>{\chi\:}_{2}>{\chi\:}_{3}\)

LPFOWA²⁹

\(\:{u}_{1.0455}\)

\(\:{u}_{0.6306}\)

\(\:{u}_{0.5833}\)

\(\:{u}_{0.7655}\)

\(\:{\chi\:}_{1}>{\chi\:}_{4}>{\chi\:}_{2}>{\chi\:}_{3}\)

LPFOWG²⁹

\(\:{u}_{0.9542}\)

\(\:{u}_{0.5341}\)

\(\:{u}_{0.5331}\)

\(\:{u}_{0.7272}\)

\(\:{\chi\:}_{1}>{\chi\:}_{4}>{\chi\:}_{2}>{\chi\:}_{3}\)

LPFDOWA

\(\:{u}_{1.2275}\)

\(\:{u}_{0.7864}\)

\(\:{u}_{0.6561}\)

\(\:{u}_{0.8070}\)

\(\:{\chi\:}_{1}>{\chi\:}_{4}>{\chi\:}_{2}>{\chi\:}_{3}\)

LPFDOWG

\(\:{u}_{0.8597}\)

\(\:{u}_{0.4477}\)

\(\:{u}_{0.5014}\)

\(\:{u}_{0.6736}\)

\(\:{\chi\:}_{1}>{\chi\:}_{4}>{\chi\:}_{3}>{\chi\:}_{2}\)