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Table 6 Results for different reasoning schemes for A ′ ′ A

From: Similarity in fuzzy systems

Modified relation

Relation

Input data (A′)

S(A, A′)

Output (B′)

S(B, B′)

mr1

R 1

A′

0.683772

B′ ⊃ B

0.438764

 

R 2

A′

0.683772

B′ ⊃ B

0.441981

 

R 3

A′

0.683772

B′ ⊃ B

0.437005

 

R 4

A′

0.683772

B′=B

1.0

 

R 5

A′

0.683772

B′ ⊃ B

0.935526

 

R 6

A′

0.683772

B′ ⊃ B

0.906437

 

R 7

A′

0.683772

B′ ⊃ B

0.935526

 

R 8

A′

0.683772

B′ ⊃ B

0.935526

 

R 9

A′

0.683772

B′ ⊃ B

0.935526

mr2

R 1

A′

0.683772

B′ ⊃ B

0.437789

 

R 2

A′

0.683772

B′ ⊃ B

0.439834

 

R 3

A′

0.683772

B′ ⊃ B

0.436249

 

R 4

A′

0.683772

B′ ⊃ B

0.707154

 

R 5

A′

0.683772

B′ ⊃ B

0.697115

 

R 6

A′

0.683772

B′ ⊃ B

0.691508

 

R 7

A′

0.683772

B′ ⊃ B

0.697115

 

R 8

A′

0.683772

B′ ⊃ B

0.697115

 

R 9

A′

0.683772

B′ ⊃ B

0.697115

mr3

R 1

A′

0.683772

B′ ⊃ B

0.407110

 

R 2

A′

0.683772

B′ ⊃ B

0.410883

 

R 3

A′

0.683772

B′ ⊃ B

0.405919

 

R 4

A′

0.683772

B′ ⊃ B

0.701754

 

R 5

A′

0.683772

B′ ⊃ B

0.687924

 

R 6

A′

0.683772

B′ ⊃ B

0.682404

 

R 7

A′

0.683772

B′ ⊃ B

0.687924

 

R 8

A′

0.683772

B′ ⊃ B

0.687924

 

R 9

A′

0.683772

B′ ⊃ B

0.687924

mr4

 

A′

0.683772

B′ ⊃ B

0.440355

mr5

 

A′

0.683772

B′ ⊃ B

0.440355

mr6

 

A′

0.683772

B′ ⊃ B

0.525030

mr7

 

A′

0.683772

B′ ⊃ B

0.437789