PAMSSEM I - Procédure d'Agrégation Multicritère

1. 1. Local outranking index per criterion pair.

   $$S_j(A_i,A_l)\in [0,1]$$

2. 2. Concordance index C(A_i,A_l) = Σ_{j: A_i≽A_l} w_j / Σ w_j.

   $$C(A_i,A_l)=\frac{{\sum }_{j:A_i⪰A_l}{w}_j}{{\sum }_{j=1}^n{w}_j}$$

3. 3. Local discordance index d_j(A_i,A_l) measuring how strongly A_l beats A_i on criterion j.

   $$d_j(A_i,A_l)=\frac{\max (0,C_j(A_l)-C_j(A_i))}{{\Delta }_j}$$

4. 4. Comprehensive outranking degree S(A_i,A_l) combining concordance and discordance.

   $$S(A_i,A_l)=C(A_i,A_l)\prod _{\{j:d_j>C\}}\frac{1-d_j(A_i,A_l)}{1-C(A_i,A_l)}$$

5. 5. Positive φ^+ and negative φ^- flows.

   $${\varphi }^{+}(A_i)=\sum _{l\ne i}S(A_i,A_l),{\varphi }^{-}(A_i)=\sum _{l\ne i}S(A_l,A_i)$$

6. 6. Net flow φ(A_i) = φ^+(A_i) − φ^-(A_i).

   $$\varphi (A_i)={\varphi }^{+}(A_i)-{\varphi }^{-}(A_i)$$

7. 7. PAMSSEM I partial ranking from (φ^+, φ^-); PAMSSEM II full ranking from φ descending.

   $$\text{PAMSSEM I: }({\varphi }^{+},{\varphi }^{-})\text{ partial};\text{PAMSSEM II: rank by }\varphi \text{ descending}$$