N-GRA - Neutrosophic extension of GRA

1. 1. SVN matrix; cost complement for cost criteria.

   $$\mathbf{D}=(⟨T_{ij},I_{ij},F_{ij}⟩);\text{cost: }{\tilde{a}}_{ij}^c=⟨F_{ij},1-I_{ij},T_{ij}⟩$$

2. 2. Neutrosophic ideal reference sequence.

   $${\alpha }_j^0=⟨\underset{i}{\max }{T}_{ij},\underset{i}{\min }{I}_{ij},\underset{i}{\min }{F}_{ij}⟩,j=1,\dots ,n$$

3. 3. Neutrosophic Euclidean distances to ideal; global extremes.

   $${\Delta }_{ij}=\sqrt{\frac{({\max }_k{T}_{kj}-T_{ij}{)}^2+({\min }_k{I}_{kj}-I_{ij}{)}^2+({\min }_k{F}_{kj}-F_{ij}{)}^2}{3}};{\Delta }_{\min }=\underset{i}{\min }\underset{j}{\min }{\Delta }_{ij};{\Delta }_{\max }=\underset{i}{\max }\underset{j}{\max }{\Delta }_{ij}$$

4. 4. Grey Relational Coefficient with ρ=0.5.

   $${\xi }_{ij}=\frac{{\Delta }_{\min }+\rho {\Delta }_{\max }}{{\Delta }_{ij}+\rho {\Delta }_{\max }},\rho =0.5$$

5. 5. Grey Relational Grade; rank descending.

   $${\Gamma }_i=\sum _{j=1}^n{w}_j{\xi }_{ij};\text{rank descending}$$