A risky multi-criteria decision-making approach under language environment

Abstract

We propose a decision-making approach based on the prospect theory and the cloud model for risky multi-criteria decision-making problem in which the criteria value of alternatives are uncertain and the linguistic variables and criteria's weights are partially unknown. In this method, the linguistic variables are converted into a cloud model. To address the shortcomings of the existing cloud generating method, a new method is developed based on the golden segmentation ratio and the cloud's rule of `3En'. And then, another method for measuring the distance among clouds and the degree of possibility of the cloud model is given to apply Prospect Theory to the linguistic environment. Furthermore, the treatment of other alternative solutions as dynamic reference points is considered. Based on the algorithm of maximizing deviation, the optimal model balances the subjective and objective information and through this model, the optimal criteria weights and the integrated prospect value of each solution are obtained. Finally, these solutions are ordered on the principle that the bigger the integrated prospect value is, the more optimal the solution will be. At the end of this paper, we use an example to examine the rationality and reliability of the given method.