Research on the stochastic hybrid multi-attribute decision making method based on prospect theory

With respect to stochastic hybrid multi-attribute decision making problems with interval probability and unknown attribute weight, a multi-attribute decision making method, based on the prospect theory, is proposed. to begin with, the hybrid attribute values, including real numbers, interval numbers, triangular fuzzy numbers, linguistic variables, uncertain linguistic variables and intuitionistic fuzzy values are converted to trapezoidal fuzzy numbers, and interval probability is expressed by trapezoidal fuzzy probability. the prospect value function of the trapezoidal fuzzy numbers for every alternative, under every attribute, and every natural state, based on the decision-making reference point of each attribute and the weight function of trapezoidal fuzzy probability, is constructed, and, then, the prospect value of the attribute for every alternative is calculated through the prospect value function and the weight function. then, a maximizing deviation method is used to determine the attribute weights and the weighted prospect value of the alternative is obtained by weighing the prospect values. all the alternatives are ranked according to the expected values of the weighted prospect values. finally, an illustrate example is given to show the decision-making steps, and the influence on decision making of different parameter values in value and weight functions and different decision-making reference points.