Lattice order group decision making with interval probability based on prospect theory

A random lattice order decision analysis method is proposed based on an interval probability distribution preference vector by way of entropy theory, focusing on a decision preference system in which preference relation probability is described by interval values and the DM's behavior is also considered. The preference characterization of decision makers is extended from four varieties of relations to seven varieties of preference relations. In addition to the concept, property, and operation rules of interval probability, the concept of interval-valued distribution preference vectors and the relative entropy on the lattice-ordered preference system are given. Then, the interval probability can be more precisely determined, and the weighting interval probability is transformed into the interval probability weight. The ER nonlinear optimization model based on preference entropy is established, individual preferences are aggregated by applying the priority rule and the intersection rule, and the specific steps of decision making are given. Finally, the feasibility and effectiveness of the approach proposed in this paper are illustrated with a numerical example.