Hellwig's Method - Development Pattern

1. 1. Standardise each criterion: z_ij = (x_ij − μ_j)/σ_j.

   $$z_{ij}=\frac{x_{ij}-{\mu }_j}{{\sigma }_j}$$

2. 2. Reference pattern z_0j = max z_ij (benefit) or min (cost).

   $$z_{0j}=\underset{i}{\max }{z}_{ij}(J^{+})\text{or}\underset{i}{\min }{z}_{ij}(J^{-})$$

3. 3. Euclidean distance from reference: d_i = √Σ (z_ij − z_0j)².

   $$d_{i0}=\sqrt{\sum _{j=1}^n(z_{ij}-z_{0j}{)}^2}$$

4. 4. Hellwig measure h_i = 1 − d_i/d_0; d_0 = μ_d + 2σ_d; descending ranking.

   $$h_i=1-\frac{d_{i0}}{d_0},d_0=\bar{d}+2{\sigma }_d$$