PF-MOORA - Pythagorean extension of MOORA

1. 1. PF scores; shift; vector normalisation.

   $$s_{ij}={\mu }_{ij}^2-{\nu }_{ij}^2;{\tilde{s}}_{ij}=s_{ij}+1;{\bar{s}}_{ij}={\tilde{s}}_{ij}/\sqrt{\sum _i{\tilde{s}}_{ij}^2}$$

2. 2. Ratio system.

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

3. 3. Reference point (optional).

   $$r_j^{\ast }=\underset{i}{\max }{\bar{s}}_{ij}(j\in {\Omega }_b);y_i^{\ast \ast }=\underset{j}{\max }{w}_j|r_j^{\ast }-{\bar{s}}_{ij}|;\text{rank ascending}$$

4. 4. Final ranking from RS.

   $$\text{rank by }{y}_i^{\ast }\text{ (descending)}$$

5. 5. Final ranking output.

   $$A_{\sigma (1)}\succ \cdots \succ A_{\sigma (m)}$$