PSI - Issue 72

Ruhit Bardhan et al. / Procedia Structural Integrity 72 (2025) 507–519

513

1

K

 

(13)

T

T

ij

1 k ijk 

K

1

K

 

(14)

I

I

ij

1 k ijk 

K

1

K

 

1 k ijk  (15) where is the number of evaluation points along the gradient, and ( , , ) is the neutrosophic evaluation at point for alternative under criterion . Step 2: Normalization of Neutrosophic Decision Matrix. We normalize the neutrosophic choice matrix to improve compatibility across various criterion scales. Normalization modifies the magnitudes of the SVNVs while maintaining their structure for neutrosophic values. For benefit criteria (where higher values are preferred):   , , ij ij ij ij r T I F  (16) ij F F K

For cost criteria (where lower values are preferred):   ,1 , ij ij ij ij r T I F  

(17)

Step 3: Computation of the neutrosophic decision matrix with weighted normalization.

The criteria weights are included in the computation of the weighted normalized neutrosophic decision matrix:

w

w









w

  

  

j

j

j

,1 1

,1 1

v w r

T

I

F

  

 

 

(18)

ij

j

ij

ij

ij

ij

where is the weight of criterion with ∑ =1 = 1 . Step 4: Determination of Neutrosophic Ideal Solutions The NPIS and NNIS are defined as:   1 2 , ,..., n A v v v     

(19)

  1 2 , ,..., n A v v v     

(20)

where:













(21)

1 1,0,0 and v

0, 0,1 for all

v

j





1

Step 5: Calculation of Separation Measures.