qR-MOORA - q-Rung Orthopair extension of MOORA

1. 1. Compute q-ROF score and shift to positive range: s_ij = μ_ij^q - ν_ij^q ∈ [-1,1]; s̃_ij = s_ij + 1 ∈ [0,2]. Shift ensures positive values for vector normalization.

   $$s_{ij}={\mu }_{ij}^q-{\nu }_{ij}^q\in [-1,1];{\tilde{s}}_{ij}=s_{ij}+1\in [0,2]$$

2. 2. Vector normalization on shifted scores: s̄_ij = s̃_ij / √(Σ_i s̃_ij²).

   $${\bar{s}}_{ij}=\frac{{\tilde{s}}_{ij}}{\sqrt{{\sum }_{i=1}^m{\tilde{s}}_{ij}^2}}$$

3. 3. Ratio System: weighted net assessment y_i* = Σ_{j∈Ω_b} w_j s̄_ij - Σ_{j∈Ω_c} w_j s̄_ij. Rank descending.

   $$y_i^{\ast }=\sum _{j\in {\Omega }_b}{w}_j{\bar{s}}_{ij}-\sum _{j\in {\Omega }_c}{w}_j{\bar{s}}_{ij};\text{rank descending}$$

4. 4. Reference Point (optional): r_j* = max s̄_ij (j∈Ω_b) or min s̄_ij (j∈Ω_c). Chebyshev distance: y_i** = max_j w_j|r_j* - s̄_ij|. Rank ascending.

   $$r_j^{\ast }=\{\begin{array}{ll}{\max }_i{\bar{s}}_{ij}& j\in {\Omega }_b\\ {\min }_i{\bar{s}}_{ij}& j\in {\Omega }_c\end{array};y_i^{\ast \ast }=\underset{j}{\max }{w}_j|r_j^{\ast }-{\bar{s}}_{ij}|;\text{rank ascending}$$