Grey Stochastic Multi-criteria Decision-making Approach Based on Prospect Theory and Distance Measures

Extended grey numbers (EGNs), integrated with discrete and continuous grey numbers, have a powerful capability in expressing uncertainty. Considering the grey and randomness of multi-criteria decision-making (MCDM) problems and the limitation of human knowledge, a grey stochastic MCDM approach based on prospect theory and distance measures is proposed, in which the criteria values take the form of EGNs. Firstly, a new order relationship of EGNs is defined, and the generalized distance measures of EGNs as well as their properties are introduced. Then the value function of EGNs based on a plurality of reference points and the weight function are constructed. After calculation, the prospect value for each alternative concerning each criterion is obtained, which is in the form of EGNs. Furthermore, based on the distance measures of EGNs and TODIM, all the alternatives are ranked according to their global value. Finally, two illustrate examples show the feasibility and usability of the proposed approach, and comparison analysis with the existing method is made.