Table 3 Comparison of the IFSM with existing ones for Example 2.

\(M_{i}\)

\(\{\langle 0.0,0.0\rangle \}\)

\(\{\langle 0.0,0.0\rangle \}\)

\(\{\langle 0.82,0.09 \rangle \}\)

\(\{\langle 0.82,0.09 \rangle \}\)

\(\{\langle 0.82,0.09 \rangle \}\)

\(N_{i}\)

\(\{\langle 0.5,0.5\rangle \}\)

\(\{\langle 0.6,0.4\rangle \}\)

\(\{\langle 0.78,0.12\rangle \}\)

\(\{\langle 0.77,0.09 \rangle \}\)

\(\{\langle 0.78,0.08\rangle \}\)

\(S_H\)

Hong and Kim²⁷

0.5000

0.5000

0.9650

0.9750

0.9750

\(S_{DC}\)

Dengfeng and Chuntian²⁹

1.0000

0.9000

0.9650

0.9750

0.9850

\(S_M\)

Mitchell³⁰

0.2929

0.2965

0.8134

0.8882

0.8500

\(S_{WX}\)

Wang and Xin³²

0.5000

0.4500

0.9625

0.9625

0.9675

\(S_{VS}\)

Vlachos and Sergiadis³⁷

NaN

NaN

0.9973

0.9992

0.9992

\(S_{HY}^{1}\)

Hung and Yang³⁵

0.0000

0.0000

0.9255

0.9451

0.9451

\(S_{HY}^{2}\)

Hung and Yang³⁵

0.5000

0.5000

0.9650

0.9750

0.9750

\(S_{HY}^{3}\)

Hung and Yang³⁵

0.0000

0.0000

0.9255

0.9451

0.9451

\(S_{HY}^{4}\)

Hung and Yang³⁵

0.0000

0.0000

0.9613

0.9718

0.9718

\(S_{YC}\)

Yang and Chiclana³⁸

0.0000

0.0000

0.9656

0.9495

0.9495

\(S_{Y}\)

Ye³⁹

NaN

NaN

0.9991

1.0000

1.0000

\(S_{BA}\)

Boran and Akay⁴⁰

0.7643

0.7643

0.8920

0.9087

0.9293

\(S_{Y1}\)

Ye⁴¹

0.0000

0.0000

0.9980

0.9969

0.9969

\(S_{Y2}\)

Ye⁴¹

0.0000

0.0000

0.9980

0.9969

0.9969

\(S_{x}\)

Xiao⁴²

NaN

NaN

0.9618

0.9440

0.9440

\(S_{MP}\)

Mahnta and Panda⁴³

0.0000

0.0000

0.9613

0.9718

0.9718

\(S_{P}^{1}\)

Patel et al.⁴⁴

0.2075

0.1995

0.9987

0.9974

0.9977

\(S_{G}\)

Gohain et al.⁵⁷

0.8718

0.7881

0.9649

0.9749

0.9748

\(S_{Z}\)

Zeng et al.⁴⁶

0.8161

0.8161

0.9733

0.9809

0.9809

\(S_{P}^2\)

Patel et al.⁶

0.9037

0.8875

1.0000

1.0000

1.0000

\(S_{J}\)

Jiang et al.³

0.5637

0.5542

0.9752

0.9823

0.9823

\(S_{D}\)

Dutta et al.⁴⁷

0.7273

0.6364

0.9137

0.9456

0.9456

\(S_A\)

Proposed IFSM

0.1667

0.1733

0.9475

0.9350

0.9347