Grey random dynamic multiple-attribute decision-making method

Abstract

In view of the uncertain multi-attribute decision-making problems when the state probabilities and options' attribute values are both three-parameter interval grey number, based on the application demand of risky investment decisions, a grey-stochastic risk dynamic multi-attribute decision making method based on Markov chain is proposed. The grey probability of state stochastic occurrence and the grey probability matrix of state stochastic transition are defined, then, the grey probability distribution of states at each future time is obtained based on the Markov chain transfer prediction method. Time weights are established by solving the optimization model, which is based on variance and time degree. Afterwards, the dynamic risk decision-making matrix is assembled into a static non-risk decision-making matrix. Finally, by means of constructing the optimal and inferior ideal projects, and based on Deng's grey relational analysis, the relative superior membership degree, which is used to measure the degree of each alternative project belonging to the optimal ideal project, can be figured out to rank the alternative projects. An example is presented to illustrate the effectiveness and feasibility of the proposed method.