A method of group decision-making based on preference distance of binary relation

Deriving the “closest” (minimal distance) collective judgment to all individual opinions is a complex aggregation problem that has been widely studied in group decision-making literature. However, most of the existing literature does not consider individual opinions expressed as partial preorders (i.e., a preference system which includes the incomparability relation), say nothing of lattice orders. In this paper, we propose a new method in which group decision-making problem based on preference distance when the preference information is provided by decision makers with lattice order preference structure. For this purpose, we first extend preference relations with preorder structure to lattice order structure, built a distance measure between pairs of binary relations in order to quantify the divergence between two lattice orders. Using the distance of preference relation, a mathematical model is established, the individual preferences are aggregated by applying the priority rules and intersection rules, and the group's preference structure has partial order characteristic. An algorithm for the aggregation procedure is proposed, followed by a numerical illustration.