Table 1 CTSHF decision-matrix.

From: 3D seismic analysis of mine planning using Aczel–Alsina aggregation operators based on T-spherical fuzzy information

 

\({\widehat{{\varvec{\eta}}}}_{{\varvec{p}}}^{1}\)

\({\widehat{{\varvec{\eta}}}}_{{\varvec{p}}}^{2}\)

\({\widehat{{\varvec{\eta}}}}_{{\varvec{p}}}^{{\varvec{A}}-1}\)

\(\left(\begin{array}{c}\left\{{\rm O}.2{\mathcal{e}}^{i2\Pi \left({\rm O}.3\right)},{\rm O}.4{\mathcal{e}}^{i2\Pi \left({\rm O}.7\right)},{\rm O}.7{\mathcal{e}}^{i2\Pi \left({\rm O}.8\right)}\right\},\\ \left\{{\rm O}.2{\mathcal{e}}^{i2\Pi \left({\rm O}.3\right)}\right\},\\ \left\{{\rm O}.6{\mathcal{e}}^{i2\Pi \left({\rm O}.5\right)},{\rm O}.7{\mathcal{e}}^{i2\Pi \left({\rm O}.5\right)}\right\}\end{array}\right)\)

\(\left(\begin{array}{c}\left\{{\rm O}.21{\mathcal{e}}^{i2\Pi \left({\rm O}.31\right)},{\rm O}.41{\mathcal{e}}^{i2\Pi \left({\rm O}.71\right)},{\rm O}.71{\mathcal{e}}^{i2\Pi \left({\rm O}.81\right)}\right\},\\ \left\{{\rm O}.21{\mathcal{e}}^{i2\Pi \left({\rm O}.31\right)}\right\},\\ \left\{{\rm O}.6{1\mathcal{e}}^{i2\Pi \left({\rm O}.51\right)},{\rm O}.71{\mathcal{e}}^{i2\Pi \left({\rm O}.51\right)}\right\}\end{array}\right)\)

\({\widehat{{\varvec{\eta}}}}_{{\varvec{p}}}^{{\varvec{A}}-2}\)

\(\left(\begin{array}{c}\left\{{\rm O}.1{\mathcal{e}}^{i2\Pi \left({\rm O}.7\right)},{\rm O}.3{\mathcal{e}}^{i2\Pi \left({\rm O}.5\right)},{\rm O}.6{\mathcal{e}}^{i2\Pi \left({\rm O}.8\right)}\right\},\\ \left\{{\rm O}.4{\mathcal{e}}^{i2\Pi \left({\rm O}.2\right)}\right\},\\ \left\{{\rm O}.3{\mathcal{e}}^{i2\Pi \left({\rm O}.4\right)},{\rm O}.3{\mathcal{e}}^{i2\Pi \left({\rm O}.1\right)}\right\}\end{array}\right)\)

\(\left(\begin{array}{c}\left\{{\rm O}.11{\mathcal{e}}^{i2\Pi \left({\rm O}.71\right)},{\rm O}.31{\mathcal{e}}^{i2\Pi \left({\rm O}.51\right)},{\rm O}.61{\mathcal{e}}^{i2\Pi \left({\rm O}.81\right)}\right\},\\ \left\{{\rm O}.41{\mathcal{e}}^{i2\Pi \left({\rm O}.21\right)}\right\},\\ \left\{{\rm O}.31{\mathcal{e}}^{i2\Pi \left({\rm O}.41\right)},{\rm O}.31{\mathcal{e}}^{i2\Pi \left({\rm O}.11\right)}\right\}\end{array}\right)\)

\({\widehat{{\varvec{\eta}}}}_{{\varvec{p}}}^{{\varvec{A}}-3}\)

\(\left(\begin{array}{c}\left\{{\rm O}.2{\mathcal{e}}^{i2\Pi \left({\rm O}.3\right)},{\rm O}.1{\mathcal{e}}^{i2\Pi \left({\rm O}.4\right)},{\rm O}.8{\mathcal{e}}^{i2\Pi \left({\rm O}.5\right)}\right\},\\ \left\{{\rm O}.3{\mathcal{e}}^{i2\Pi \left({\rm O}.5\right)}\right\},\\ \left\{{\rm O}.4{\mathcal{e}}^{i2\Pi \left({\rm O}.3\right)},{\rm O}.7{\mathcal{e}}^{i2\Pi \left({\rm O}.7\right)}\right\}\end{array}\right)\)

\(\left(\begin{array}{c}\left\{{\rm O}.21{\mathcal{e}}^{i2\Pi \left({\rm O}.31\right)},{\rm O}.11{\mathcal{e}}^{i2\Pi \left({\rm O}.41\right)},{\rm O}.81{\mathcal{e}}^{i2\Pi \left({\rm O}.51\right)}\right\},\\ \left\{{\rm O}.3{1\mathcal{e}}^{i2\Pi \left({\rm O}.51\right)}\right\},\\ \left\{{\rm O}.4{1\mathcal{e}}^{i2\Pi \left({\rm O}.31\right)},{\rm O}.71{\mathcal{e}}^{i2\Pi \left({\rm O}.71\right)}\right\}\end{array}\right)\)

\({\widehat{{\varvec{\eta}}}}_{{\varvec{p}}}^{{\varvec{A}}-4}\)

\(\left(\begin{array}{c}\left\{{\rm O}.1{\mathcal{e}}^{i2\Pi \left({\rm O}.5\right)},{\rm O}.6{\mathcal{e}}^{i2\Pi \left({\rm O}.3\right)},{\rm O}.6{\mathcal{e}}^{i2\Pi \left({\rm O}.8\right)}\right\},\\ \left\{{\rm O}.7{\mathcal{e}}^{i2\Pi \left({\rm O}.3\right)}\right\},\\ \left\{{\rm O}.8{\mathcal{e}}^{i2\Pi \left({\rm O}.6\right)},{\rm O}.9{\mathcal{e}}^{i2\Pi \left({\rm O}.3\right)}\right\}\end{array}\right)\)

\(\left(\begin{array}{c}\left\{{\rm O}.11{\mathcal{e}}^{i2\Pi \left({\rm O}.51\right)},{\rm O}.61{\mathcal{e}}^{i2\Pi \left({\rm O}.31\right)},{\rm O}.6{1\mathcal{e}}^{i2\Pi \left({\rm O}.81\right)}\right\},\\ \left\{{\rm O}.71{\mathcal{e}}^{i2\Pi \left({\rm O}.31\right)}\right\},\\ \left\{{\rm O}.8{1\mathcal{e}}^{i2\Pi \left({\rm O}.61\right)},{\rm O}.91{\mathcal{e}}^{i2\Pi \left({\rm O}.31\right)}\right\}\end{array}\right)\)

\({\widehat{{\varvec{\eta}}}}_{{\varvec{p}}}^{{\varvec{A}}-5}\)

\(\left(\begin{array}{c}\left\{{\rm O}.5{\mathcal{e}}^{i2\Pi \left({\rm O}.6\right)},{\rm O}.3{\mathcal{e}}^{i2\Pi \left({\rm O}.4\right)},{\rm O}.2{\mathcal{e}}^{i2\Pi \left({\rm O}.9\right)}\right\},\\ \left\{{\rm O}.5{\mathcal{e}}^{i2\Pi \left({\rm O}.4\right)}\right\},\\ \left\{{\rm O}.9{\mathcal{e}}^{i2\Pi \left({\rm O}.3\right)},{\rm O}.5{\mathcal{e}}^{i2\Pi \left({\rm O}.4\right)}\right\}\end{array}\right)\)

\(\left(\begin{array}{c}\left\{{\rm O}.51{\mathcal{e}}^{i2\Pi \left({\rm O}.61\right)},{\rm O}.3{1\mathcal{e}}^{i2\Pi \left({\rm O}.41\right)},{\rm O}.21{\mathcal{e}}^{i2\Pi \left({\rm O}.91\right)}\right\},\\ \left\{{\rm O}.51{\mathcal{e}}^{i2\Pi \left({\rm O}.41\right)}\right\},\\ \left\{{\rm O}.91{\mathcal{e}}^{i2\Pi \left({\rm O}.31\right)},{\rm O}.5{1\mathcal{e}}^{i2\Pi \left({\rm O}.41\right)}\right\}\end{array}\right)\)

 

\({\widehat{{\varvec{\eta}}}}_{{\varvec{p}}}^{3}\)

\({\widehat{{\varvec{\eta}}}}_{{\varvec{p}}}^{4}\)

\({\widehat{{\varvec{\eta}}}}_{{\varvec{p}}}^{{\varvec{A}}-1}\)

\(\left(\begin{array}{c}\left\{{\rm O}.22{\mathcal{e}}^{i2\Pi \left({\rm O}.32\right)},{\rm O}.42{\mathcal{e}}^{i2\Pi \left({\rm O}.72\right)},{\rm O}.72{\mathcal{e}}^{i2\Pi \left({\rm O}.82\right)}\right\},\\ \left\{{\rm O}.22{\mathcal{e}}^{i2\Pi \left({\rm O}.32\right)}\right\},\\ \left\{{\rm O}.6{2\mathcal{e}}^{i2\Pi \left({\rm O}.52\right)},{\rm O}.72{\mathcal{e}}^{i2\Pi \left({\rm O}.52\right)}\right\}\end{array}\right)\)

\(\left(\begin{array}{c}\left\{{\rm O}.23{\mathcal{e}}^{i2\Pi \left({\rm O}.33\right)},{\rm O}.43{\mathcal{e}}^{i2\Pi \left({\rm O}.73\right)},{\rm O}.73{\mathcal{e}}^{i2\Pi \left({\rm O}.83\right)}\right\},\\ \left\{{\rm O}.23{\mathcal{e}}^{i2\Pi \left({\rm O}.33\right)}\right\},\\ \left\{{\rm O}.6{3\mathcal{e}}^{i2\Pi \left({\rm O}.53\right)},{\rm O}.73{\mathcal{e}}^{i2\Pi \left({\rm O}.53\right)}\right\}\end{array}\right)\)

\({\widehat{{\varvec{\eta}}}}_{{\varvec{p}}}^{{\varvec{A}}-2}\)

\(\left(\begin{array}{c}\left\{{\rm O}.12{\mathcal{e}}^{i2\Pi \left({\rm O}.72\right)},{\rm O}.32{\mathcal{e}}^{i2\Pi \left({\rm O}.52\right)},{\rm O}.62{\mathcal{e}}^{i2\Pi \left({\rm O}.82\right)}\right\},\\ \left\{{\rm O}.42{\mathcal{e}}^{i2\Pi \left({\rm O}.22\right)}\right\},\\ \left\{{\rm O}.32{\mathcal{e}}^{i2\Pi \left({\rm O}.42\right)},{\rm O}.32{\mathcal{e}}^{i2\Pi \left({\rm O}.12\right)}\right\}\end{array}\right)\)

\(\left(\begin{array}{c}\left\{{\rm O}.13{\mathcal{e}}^{i2\Pi \left({\rm O}.73\right)},{\rm O}.33{\mathcal{e}}^{i2\Pi \left({\rm O}.53\right)},{\rm O}.63{\mathcal{e}}^{i2\Pi \left({\rm O}.83\right)}\right\},\\ \left\{{\rm O}.43{\mathcal{e}}^{i2\Pi \left({\rm O}.23\right)}\right\},\\ \left\{{\rm O}.33{\mathcal{e}}^{i2\Pi \left({\rm O}.43\right)},{\rm O}.33{\mathcal{e}}^{i2\Pi \left({\rm O}.13\right)}\right\}\end{array}\right)\)

\({\widehat{{\varvec{\eta}}}}_{{\varvec{p}}}^{{\varvec{A}}-3}\)

\(\left(\begin{array}{c}\left\{{\rm O}.22{\mathcal{e}}^{i2\Pi \left({\rm O}.32\right)},{\rm O}.12{\mathcal{e}}^{i2\Pi \left({\rm O}.42\right)},{\rm O}.82{\mathcal{e}}^{i2\Pi \left({\rm O}.52\right)}\right\},\\ \left\{{\rm O}.3{2\mathcal{e}}^{i2\Pi \left({\rm O}.52\right)}\right\},\\ \left\{{\rm O}.4{2\mathcal{e}}^{i2\Pi \left({\rm O}.32\right)},{\rm O}.72{\mathcal{e}}^{i2\Pi \left({\rm O}.72\right)}\right\}\end{array}\right)\)

\(\left(\begin{array}{c}\left\{{\rm O}.23{\mathcal{e}}^{i2\Pi \left({\rm O}.33\right)},{\rm O}.13{\mathcal{e}}^{i2\Pi \left({\rm O}.43\right)},{\rm O}.83{\mathcal{e}}^{i2\Pi \left({\rm O}.53\right)}\right\},\\ \left\{{\rm O}.3{3\mathcal{e}}^{i2\Pi \left({\rm O}.53\right)}\right\},\\ \left\{{\rm O}.4{3\mathcal{e}}^{i2\Pi \left({\rm O}.33\right)},{\rm O}.73{\mathcal{e}}^{i2\Pi \left({\rm O}.73\right)}\right\}\end{array}\right)\)

\({\widehat{{\varvec{\eta}}}}_{{\varvec{p}}}^{{\varvec{A}}-4}\)

\(\left(\begin{array}{c}\left\{{\rm O}.12{\mathcal{e}}^{i2\Pi \left({\rm O}.52\right)},{\rm O}.62{\mathcal{e}}^{i2\Pi \left({\rm O}.32\right)},{\rm O}.6{2\mathcal{e}}^{i2\Pi \left({\rm O}.82\right)}\right\},\\ \left\{{\rm O}.72{\mathcal{e}}^{i2\Pi \left({\rm O}.32\right)}\right\},\\ \left\{{\rm O}.8{2\mathcal{e}}^{i2\Pi \left({\rm O}.62\right)},{\rm O}.92{\mathcal{e}}^{i2\Pi \left({\rm O}.32\right)}\right\}\end{array}\right)\)

\(\left(\begin{array}{c}\left\{{\rm O}.13{\mathcal{e}}^{i2\Pi \left({\rm O}.53\right)},{\rm O}.63{\mathcal{e}}^{i2\Pi \left({\rm O}.33\right)},{\rm O}.6{3\mathcal{e}}^{i2\Pi \left({\rm O}.83\right)}\right\},\\ \left\{{\rm O}.73{\mathcal{e}}^{i2\Pi \left({\rm O}.33\right)}\right\},\\ \left\{{\rm O}.8{3\mathcal{e}}^{i2\Pi \left({\rm O}.63\right)},{\rm O}.93{\mathcal{e}}^{i2\Pi \left({\rm O}.33\right)}\right\}\end{array}\right)\)

\({\widehat{{\varvec{\eta}}}}_{{\varvec{p}}}^{{\varvec{A}}-5}\)

\(\left(\begin{array}{c}\left\{{\rm O}.52{\mathcal{e}}^{i2\Pi \left({\rm O}.62\right)},{\rm O}.3{2\mathcal{e}}^{i2\Pi \left({\rm O}.42\right)},{\rm O}.22{\mathcal{e}}^{i2\Pi \left({\rm O}.92\right)}\right\},\\ \left\{{\rm O}.52{\mathcal{e}}^{i2\Pi \left({\rm O}.42\right)}\right\},\\ \left\{{\rm O}.92{\mathcal{e}}^{i2\Pi \left({\rm O}.32\right)},{\rm O}.5{2\mathcal{e}}^{i2\Pi \left({\rm O}.42\right)}\right\}\end{array}\right)\)

\(\left(\begin{array}{c}\left\{{\rm O}.53{\mathcal{e}}^{i2\Pi \left({\rm O}.63\right)},{\rm O}.3{3\mathcal{e}}^{i2\Pi \left({\rm O}.43\right)},{\rm O}.23{\mathcal{e}}^{i2\Pi \left({\rm O}.93\right)}\right\},\\ \left\{{\rm O}.53{\mathcal{e}}^{i2\Pi \left({\rm O}.43\right)}\right\},\\ \left\{{\rm O}.93{\mathcal{e}}^{i2\Pi \left({\rm O}.33\right)},{\rm O}.5{3\mathcal{e}}^{i2\Pi \left({\rm O}.43\right)}\right\}\end{array}\right)\)

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