Scenario Fuzzy GRA - Derived TFN Component-Scenario Profile

1. 1. Validate and capture a pre-aggregated ordered TFN decision matrix.

   $$\tilde{X}=[(x_{ij}^L,x_{ij}^M,x_{ij}^U)],x_{ij}^L\le x_{ij}^M\le x_{ij}^U$$

2. 2. Run direction-aware crisp GRA independently on lower, modal, and upper component matrices using the same crisp weight vector and rho.

   $$S_i^{(s)}=scal{e}_{[0,1]}(\sum _j{w}_j\frac{{\Delta }_{min}^{(s)}+\rho {\Delta }_{max}^{(s)}}{{\Delta }_{ij}^{(s)}+\rho {\Delta }_{max}^{(s)}+ϵ}),s\in \{L,M,U\}$$

3. 3. Average the three independently scaled component scores and rank alternatives in descending stable order.

   $$S_i=\frac{S_i^{(L)}+S_i^{(M)}+S_i^{(U)}}{3},rank=sor{t}_{desc}(S)$$