Research on the Stochastic Hybrid Multi-attribute Decision Making Method Based on Prospect Theory

Abstract

With respect to the stochastic hybrid multi-attribute decision making problems with interval probability and unknown attribute weight, a multi-attribute decision making method based on prospect theory is proposed. To begin with, the hybrid attribute vales, including real numbers, interval numbers, triangular fuzzy numbers, linguistic variables, uncertain linguistic variables and intuitionistic fuzzy values, are converted to trapezoidal fuzzy numbers, and intervalprobability is expressed by trapezoidal fuzzyprobability; the prospectvalue function of the trapezoidal fuzzy numbers for every alternative under every attribute and everynatural state based on the decision-making reference point of each attribute, and the weight function of trapezoidal fuzzyprobability,can be constructed; then the prospect value of attribute for every alternative is calculated through prospectvalue function and the weight function. Then, a maximizing deviation method is used to determine the attribute weightsand the weighted prospect value of alternative is get by weighting the prospect values, and 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, the influence on decision making for different parameter values in value function and weight function and different decision-making reference points. ing