Alternatives ranking in preference ordering-based group decision making: Complementary judgment matrix approach

The use of complementary judgment matrixes as alternatives ranking method in preference ordering-based group decision making is studied. Firstly, judgment matrixes are obtained from the alternatives' preference ordering given by members of the decision group. In case there is only priority relation between two alternatives, real number complementary judgment matrix is obtained. When priority relation as well as indifference relation are included, both real number complementary judgment matrix and interval number complementary judgment matrix are constructed. Necessary conditions for the paradox of voting are obtained by applying the additive transitivity. Based on the complementary judgment matrices, goal programming models are established by the additive transitivity, from which the alternatives' ranking can be derived. Numerical example is provided. Comparing of results with that of other methods showed that the proposed method is feasible.