Table 2 Normalized CPHF decision matrix.

From: Some complex probabilistic hesitant fuzzy aggregation operators and their applications to multi-attribute decision making

U

\({x_1}\)

\({x_2}\)

\({x_3}\)

\({A_1}\)

\(\{0.6\cdot e^{i2\pi (0.2)}|0.2,0.7\cdot e^{i2\pi (0.5)}|0.8\}\)

\(\{0.7\cdot e^{i2\pi (0.6)}|0.6,0.6\cdot e^{i2\pi (0.3)}|0.4\}\)

\(\{0.2\cdot e^{i2\pi (0.4)}|1\}\)

\({A_2}\)

\(\{0.4\cdot e^{i2\pi (0.1)}|0.1,0.2\cdot e^{i2\pi (0.3)}|0.9\}\)

\(\{0.2\cdot e^{i2\pi (0.5)}|1\}\)

\(\{0.3\cdot e^{i2\pi (0.3)}|0.5,0.4\cdot e^{i2\pi (0.2)}|0.5\}\)

\({A_3}\)

\(\{0.5\cdot e^{i2\pi (0.6)}|1\}\)

\(\{0.5\cdot e^{i2\pi (0.3)}|0.4,0.2\cdot e^{i2\pi (0.1)}|0.6\}\)

\(\{0.5\cdot e^{i2\pi (0.7)}|0.7,0.6\cdot e^{i2\pi (0.8)}|0.3\}\)

\(A_4\)

\(\{0.6\cdot e^{i2\pi (0.7)}|0.6,0.9\cdot e^{i2\pi (0.5)}|0.4\}\)

\(\{0.7\cdot e^{i2\pi (0.6)}|0.5,0.8\cdot e^{i2\pi (0.4)}|0.5\}\)

\(\{0.5\cdot e^{i2\pi (0.7)}|0.7,0.8\cdot e^{i2\pi (0.6)}|0.3\}\)

\(A_5\)

\(\{0.3\cdot e^{i2\pi (0.4)}|0.7,0.5\cdot e^{i2\pi (0.2)}|0.3\}\)

\(\{0.3\cdot e^{i2\pi (0.4)}|1\}\)

\(\{0.2\cdot e^{i2\pi (0.4)}|0.9,0.4\cdot e^{i2\pi (0.5)}|0.1\}\)