Table 8 Sensitivity analysis.

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

Parameter amounts

Outcomes of LFF-WASPAS method for various alternatives

Final ranking

\(\mathcal{t}=0.1\)

0.244

0.180

0.272

0.223

0.232

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

\(\mathcal{t}=0.2\)

0.247

0.182

0.273

0.224

0.234

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

\(\mathcal{t}=0.3\)

0.249

0.184

0.274

0.226

0.236

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

\(\mathcal{t}=0.4\)

0.251

0.186

0.275

0.227

0.238

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

\(\mathcal{t}=0.5\)

0.254

0.188

0.276

0.228

0.240

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

\(\mathcal{t}=0.6\)

0.256

0.190

0.277

0.229

0.242

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

\(\mathcal{t}=0.7\)

0.259

0.192

0.278

0.231

0.244

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

\(\mathcal{t}=0.8\)

0.261

0.193

0.279

0.232

0.246

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

\(\mathcal{t}=0.9\)

0.264

0.195

0.280

0.233

0.248

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

\(\mathcal{t}=1.0\)

0.266

0.197

0.281

0.234

0.250

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