A method to calculate the ranges of criteria weights in ELECTRE I and II methods

In this study, the ranges of criteria weights based on the outranking relations in ELECTRE I and II methods are analyzed, which is considered as the sensitivity analysis regarding criteria weights. First, an important theorem is proved, in which the maximum value of discordance indices for any two alternatives is shown to be equal to 1. Using this theorem, four situations of outranking relations for any two alternatives are simplified to two situations when sensitivity analysis of criteria weights is performed for ELECTRE I. Subsequently, some inequalities are obtained to calculate the ranges of criteria weights when keeping the outranking relations between any two alternatives unchanged. For ELECTRE II, nine situations of strong and weak outranking relations are simplified into three situations of relations according to this theorem. The ranges of criteria weights are also derived when the strong and weak outranking relations remain unchanged. Finally, two examples are presented to test and verify the effectiveness of the sensitivity analysis of criteria weights for ELECTRE I. Two analogous examples are also presented in ELECTRE II.