Table 9 Sensitivity Analysis.

From: Novel concept of linguistic fractional fuzzy information for effective water filtration decision-making problem based on WASPAS method

Parameter \(f\) amounts

Outcomes of LFF-WASPAS method for various alternatives

Final ranking

\(f=3/2\)

0.291

0.237

0.304

0.269

0.278

\({\mathcal{A}}_{3}\succ {\mathcal{A}}_{1}\succ {\mathcal{A}}_{5}\succ {\mathcal{A}}_{4}\succ {\mathcal{A}}_{2}\)

\(f=5/2\)

0.254

0.188

0.276

0.228

0.240

\({\mathcal{A}}_{3}\succ {\mathcal{A}}_{1}\succ {\mathcal{A}}_{5}\succ {\mathcal{A}}_{4}\succ {\mathcal{A}}_{2}\)

\(f=7/2\)

0.188

0.135

0.230

0.166

0.190

\({\mathcal{A}}_{3}\succ {\mathcal{A}}_{5}\succ {\mathcal{A}}_{1}\succ {\mathcal{A}}_{4}\succ {\mathcal{A}}_{2}\)

\(f=9/2\)

0.135

0.095

0.185

0.117

0.146

\({\mathcal{A}}_{3}\succ {\mathcal{A}}_{5}\succ {\mathcal{A}}_{1}\succ {\mathcal{A}}_{4}\succ {\mathcal{A}}_{2}\)

\(f=11/2\)

0.096

0.068

0.146

0.081

0.111

\({\mathcal{A}}_{3}\succ {\mathcal{A}}_{5}\succ {\mathcal{A}}_{1}\succ {\mathcal{A}}_{4}\succ {\mathcal{A}}_{2}\)

\(f=13/2\)

0.069

0.049

0.115

0.057

0.085

\({\mathcal{A}}_{3}\succ {\mathcal{A}}_{5}\succ {\mathcal{A}}_{1}\succ {\mathcal{A}}_{4}\succ {\mathcal{A}}_{2}\)

\(f=15/2\)

0.051

0.036

0.090

0.040

0.065

\({\mathcal{A}}_{3}\succ {\mathcal{A}}_{5}\succ {\mathcal{A}}_{1}\succ {\mathcal{A}}_{4}\succ {\mathcal{A}}_{2}\)

\(f=17/2\)

0.037

0.027

0.071

0.029

0.050

\({\mathcal{A}}_{3}\succ {\mathcal{A}}_{5}\succ {\mathcal{A}}_{1}\succ {\mathcal{A}}_{4}\succ {\mathcal{A}}_{2}\)

\(f=19/2\)

0.028

0.021

0.057

0.023

0.039

\({\mathcal{A}}_{3}\succ {\mathcal{A}}_{5}\succ {\mathcal{A}}_{1}\succ {\mathcal{A}}_{4}\succ {\mathcal{A}}_{2}\)

\(f=21/2\)

0.016

0.013

0.036

0.011

0.024

\({\mathcal{A}}_{3}\succ {\mathcal{A}}_{5}\succ {\mathcal{A}}_{1}\succ {\mathcal{A}}_{4}\succ {\mathcal{A}}_{2}\)