PF-ARAS - Pythagorean extension of ARAS

1. 1. Cost complement; optimal A0.

   $$j\in {\Omega }_c:{\hat{\alpha }}_{ij}=({\nu }_{ij},{\mu }_{ij});{\hat{\alpha }}_{0j}=(\underset{i}{\max }{\hat{\mu }}_{ij},\underset{i}{\min }{\hat{\nu }}_{ij})$$

2. 2. Column-sum normalisation on scores.

   $$s_{ij}=s({\hat{\alpha }}_{ij});{\tilde{s}}_{ij}=s_{ij}+1;{\hat{s}}_{ij}={\tilde{s}}_{ij}/\sum _{i=0}^m{\tilde{s}}_{ij}$$

3. 3. PFWA aggregate score.

   $${\tilde{S}}_i={\mathrm{PFWA}}_w({\hat{\alpha }}_{i1}^n,\dots ,{\hat{\alpha }}_{in}^n);S_i=s({\tilde{S}}_i)$$

4. 4. Degree of utility K_i.

   $$K_i=S_i/S_0$$

5. 5. Rank descending by K_i.

   $$\text{rank descending by }{K}_i$$