Random lattice order group decision-making based on interval probability preferences

To solve the random lattice order group decision-making problems where preference relations are random and probability of random events is described by interval values, a decision-making method based on the preferences of decision makers subject to an interval probability distribution is proposed. First, the preference relations are extended from four kinds (preference, inferior, indifference, and incomparability) to seven kinds (preference, inferior, indifference, incomparability, incomparability with a minimum upper bound, incomparability with a maximum lower bound, and incomparability with a minimum upper bound and a maximum lower bound). Second, the probability distribution of lattice order preference relations is defined on the basis of the concept and property of interval probability, and the operation rules of interval numbers. Third, the probability maximization objective function of preference relation of any pair of alternatives is established, and individual preferences are aggregated to group preferences according to priority rules and intersection rules. Finally, the steps of the group decision-making method are listed through a case study, and the feasibility and effectiveness of the method is validated.