A novel fuzzy TOPSIS method based on T-spherical fuzzy Aczel–Alsina power Heronian mean operators with applications in pharmaceutical enterprises’ selection

Liu, Peide; Khan, Qaisar; Jamil, Ayesha; Haq, Ijaz Ul; Sikandar, Waseem; Hussain, Fawad

doi:10.1007/s40747-023-01249-3

Table 20 Revised decision matrix \(\overline{\overline{NWDM}}^{2}\)

From: A novel fuzzy TOPSIS method based on T-spherical fuzzy Aczel–Alsina power Heronian mean operators with applications in pharmaceutical enterprises’ selection

Alternatives/criteria	\('\!O_{1}\)	\('\!O_{2}\)	\('\!O_{3}\)	\('\!O_{4}\)	\('\!O_{5}\)	\('\!O_{6}\)	\('\!O_{7}\)
\('\!\gamma_{1}\)	\(\left\langle \begin{gathered} 0.4911,0.6221, \hfill \\ 0.6221 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.4922,0.6200, \hfill \\ 0.6200 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.6839,0.4212, \hfill \\ 0.4212 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.6741,0.4403, \hfill \\ 0.4403 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.6753,0.4380, \hfill \\ 0.4380 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.4920,0.6203, \hfill \\ 0.6203 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.4967,0.6113, \hfill \\ 0.6113 \hfill \\ \end{gathered} \right\rangle\)
\('\!\gamma_{2}\)	\(\left\langle \begin{gathered} 0.4911,0.6221, \hfill \\ 0.6221 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.5817,0.5335, \hfill \\ 0.5335 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.6839,0.4212, \hfill \\ 0.4212 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.4886,0.6269, \hfill \\ 0.6269 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.4896,0.6250, \hfill \\ 0.6250 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.5815,0.5340, \hfill \\ 0.5340 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.3268,0.6113, \hfill \\ 0.7601 \hfill \\ \end{gathered} \right\rangle\)
\('\!\gamma_{3}\)	\(\left\langle \begin{gathered} 0.4058,0.6983, \hfill \\ 0.6983 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.2420,0.5335, \hfill \\ 0.8302 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.6839,0.4212, \hfill \\ 0.4212 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.6741,0.4403, \hfill \\ 0.4403 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.4896,0.6250, \hfill \\ 0.6250 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.4920,0.6203, \hfill \\ 0.6203 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.4106,0.6892, \hfill \\ 0.6892 \hfill \\ \end{gathered} \right\rangle\)
\('\!\gamma_{4}\)	\(\left\langle \begin{gathered} 0.6771,0.4344, \hfill \\ 0.4344 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.1611,0.4318, \hfill \\ 0.8901 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.4967,0.6112, \hfill \\ 0.6112 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.7862,0.3093, \hfill \\ 0.3093 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.4045,0.7008, \hfill \\ 0.7008 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.7903,0.3012, \hfill \\ 0.3012 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.3268,0.6113, \hfill \\ 0.7601 \hfill \\ \end{gathered} \right\rangle\)
\('\!\gamma_{5}\)	\(\left\langle \begin{gathered} 0.6771,0.4344, \hfill \\ 0.4344 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.5817,0.5335, \hfill \\ 0.5335 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.6839,0.4212, \hfill \\ 0.4212 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.5776,0.5414, \hfill \\ 0.5414 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.4896,0.6250, \hfill \\ 0.6250 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.6782,0.4323, \hfill \\ 0.4323 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.4106,0.6892, \hfill \\ 0.6892 \hfill \\ \end{gathered} \right\rangle\)
\('\!\gamma_{6}\)	\(\left\langle \begin{gathered} 0.5804,0.5360, \hfill \\ 0.5360 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.6784,0.4318, \hfill \\ 0.4318 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.4106,0.6891, \hfill \\ 0.6891 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.6741,0.4403, \hfill \\ 0.4403 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.7874,0.3069, \hfill \\ 0.3069 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.6782,0.4323, \hfill \\ 0.4323 \hfill \\ \end{gathered} \right\rangle\)	\(\left\langle \begin{gathered} 0.4967,0.6113, \hfill \\ 0.6113 \hfill \\ \end{gathered} \right\rangle\)

Back to article page