Table 4 Comparison of the proposed IFSM with existing ones for Example 3.

From: Similarity measure for intuitionistic fuzzy sets and its applications in pattern recognition and multimodal medical image fusion

IFSMs

Ref

\(S(M_1,N)\)

\(S(M_2,N)\)

\(S(M_3,N)\)

Selection

DOC

Comment

\(S_H\)

Hong and Kim27

0.970

0.970

0.970

-

NA

Failed to classify

\(S_D\)

Dengfeng and Chuntian29

0.970

0.968

0.970

-

NA

Failed to classify

\(S_M\)

Mitchell30

0.827

0.827

0.833

\(M_3\)

NA

Irrational

\(S_{WX}\)

Wang and Xin32

0.968

0.970

0.963

\(M_2\)

0.010

Correctly classified

\(S_{VS}\)

Vlachos and Sergiadis37

0.997

0.997

0.996

-

NA

Failed to classify

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

Hung and Yang35

0.916

0.916

0.913

-

NA

Failed to classify

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

Hung and Yang35

0.970

0.970

0.970

-

NA

Failed to classify

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

Hung and Yang35

0.458

0.457

0.457

\(M_1\)

NA

Irrational

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

Hung and Yang35

0.956

0.956

0.955

-

NA

Failed to classify

\(S_{YC}\)

Yang and Chiclana38

0.974

0.976

0.965

\(M_2\)

0.014

Correctly classified

\(S_{Y}\)

Ye39

0.996

0.996

0.996

-

NA

Failed to classify

\(S_{BA}\)

Boran and Akay40

0.900

0.900

0.900

 

NA

Failed to classify

\(S_{Y1}\)

Ye41

0.999

0.999

0.997

-

NA

Failed to classify

\(S_{Y2}\)

Ye41

0.999

0.999

0.997

-

NA

Failed to classify

\(S_{X}\)

Xiao42

0.971

0.973

0.959

\(M_2\)

0.015

Correctly classified

\(S_{MP}\)

Mahanta and Panda43

0.956

0.956

0.955

-

NA

Failed to classify

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

Patel et al.44

0.999

0.999

0.998

-

NA

Failed to classify

\(S_{G}\)

Gohain et al.57

0.969

0.969

0.969

 

NA

Failed to classify

\(S_{Z}\)

Zeng et al.46

0.987

0.988

0.987

\(M_2\)

0.001

Correctly classified

\(S_{P}^2\)

Patel et al.6

1.000

1.000

1.000

-

NA

Failed to classify

\(S_{J}\)

Jiang et al.3

0.979

0.979

0.979

 

NA

Failed to classify

\(S_{D}\)

Dutta et al47

0.927

0.928

0.928

-

NA

Failed to classify

\(S_A\)

Proposed IFSM

0.957

0.964

0.951

\(M_2\)

0.020

Correctly classified

  1.  Bold faces denote the similarity values obtained by the proposed IFSM
  2. Italic faces indicate the counter-intuitive results and violation of similarity axioms