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Table 1 Relations between alternatives in PROMETHEE partial preorder ranking

From: Multi-criteria ranking of voice transmission carriers of a telecommunication company using PROMETHEE

Preference relation

Cases

Graphical representation

\(A_kPA_l\)

\(\phi ^+(A_k) > \phi ^+(A_l)\) and \(\phi ^-(A_k) < \phi ^-(A_l)\)

\(A_k \rightarrow A_l\)

\(\phi ^+(A_k) > \phi ^+(A_l)\) and \(\phi ^-(A_k) = \phi ^-(A_l)\)

\(\phi ^+(A_k) = \phi ^+(A_l)\) and \(\phi ^-(A_k) < \phi ^-(A_l)\)

\(A_kIA_l\)

\(\phi ^+(A_k) = \phi ^+(A_l)\) and \(\phi ^-(A_k) =\phi ^-(A_l)\)

\(A_kRA_l\)

\(\phi ^+(A_k) > \phi ^+(A_l)\) and \(\phi ^-(A_k) > \phi ^-(A_l)\)

\(\phi ^+(A_l) > \phi ^+(A_k)\) and \(\phi ^-(A_l) > \phi ^-(A_k)\)