Multiple attributes group decision making based on penalty preference

To minimize individual preference on group decision making, providing a method for multiple attributes group decision making based on penalty preference of every individual decision-maker. In decision making, each decision-maker's partial information will be added in naturally. To overcome this shortcoming, penalty coefficient is introduced to modify preference, then get an OF intensity matrix of penalty preference and construct a reduced transfer-probability Markov matrix. On this condition, get partial relation of synthetic attribute of the preference of all projects.