A new belief Markov chain model and its application in inventory prediction

The Markov chain model is widely applied in many fields, especially the field of prediction. The discrete-time Markov chain (DTMC) is a common method for prediction. However, the classical DTMC model has some limitations when the system is complex with uncertain information or state space is not discrete. To address it, a new belief Markov chain (BMC) model combining Dempster-Shafer evidence theory and the DTMC is proposed. In our model, the uncertain data are allowed to be handled in the form of interval number, and the basic probability assignment is generated by an optimisation method based on the distance between interval numbers. The shortcoming of classical DTMC is overcome in the BMC model. Also, it has an efficient ability of dealing with uncertain information, including both the uncertainty of collected data and discerning states. Our model is applied to do the prediction of inventory demand and the result is close to the practical. Also, sensitivity analysis and some comparisons are accomplished to show the effectiveness and rationality of our proposed model.