Table 6 Combined matrix (using LFFWA operator).

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

 

\({\mathcal{B}}_{3}\)

\({\mathcal{B}}_{3}\)

\({\mathcal{B}}_{3}\)

\({\mathcal{B}}_{3}\)

\({\mathcal{A}}_{1}\)

\(\left({\mathcal{S}}_{4.2557}, {\mathcal{S}}_{2.2909}\right)\)

\(\left({\mathcal{S}}_{42580}, {\mathcal{S}}_{2.0000}\right)\)

\(\left({\mathcal{S}}_{2.7429}, {\mathcal{S}}_{1.5921}\right)\)

\(\left({\mathcal{S}}_{3.7403}, {\mathcal{S}}_{1.8245}\right)\)

\({\mathcal{A}}_{2}\)

\(\left({\mathcal{S}}_{27369}, {\mathcal{S}}_{1.2613}\right)\)

\(\left({\mathcal{S}}_{4.2539}, {\mathcal{S}}_{2.8777}\right)\)

\(\left({\mathcal{S}}_{2.7377}, {\mathcal{S}}_{1.5844}\right)\)

\(\left({\mathcal{S}}_{3.9052}, {\mathcal{S}}_{1.8238}\right)\)

\({\mathcal{A}}_{3}\)

\(\left({\mathcal{S}}_{3.2258}, {\mathcal{S}}_{1.4354}\right)\)

\(\left({\mathcal{S}}_{4.5423}, {\mathcal{S}}_{2.6181}\right)\)

\(\left({\mathcal{S}}_{4.2593}, {\mathcal{S}}_{2.6253}\right)\)

\(\left({\mathcal{S}}_{4.2557}, {\mathcal{S}}_{2.8909}\right)\)

\({\mathcal{A}}_{4}\)

\(\left({\mathcal{S}}_{4.0420}, {\mathcal{S}}_{1.5921}\right)\)

\(\left({\mathcal{S}}_{3.4090}, {\mathcal{S}}_{2.0083}\right)\)

\(\left({\mathcal{S}}_{3.5815}, {\mathcal{S}}_{2.6189}\right)\)

\(\left({\mathcal{S}}_{3.7403}, {\mathcal{S}}_{1.5844}\right)\)

\({\mathcal{A}}_{5}\)

\(\left({\mathcal{S}}_{3.5902}, {\mathcal{S}}_{1.8118}\right)\)

\(\left({\mathcal{S}}_{3.2215}, {\mathcal{S}}_{1.8149}\right)\)

\(\left({\mathcal{S}}_{4.5406}, {\mathcal{S}}_{1.8149}\right)\)

\(\left({\mathcal{S}}_{3.9048}, {\mathcal{S}}_{2.8847}\right)\)