A belief Markov model and its application

Markov chain is widely applied to the fields of natural science and engineering technology with its non-aftereffect property. However, the classical Markov chain is unable to handle the uncertainty of state description. Besides, the state's transition is unstable when the divide boundary of states is too clear. In order to overcome these limitations, a belief Markov model is proposed in this paper. Dempster-Shafer (DS) theory of evi-dence is introduced to new model to represent the uncertainty of states. Firstly, the states are reduced to form a frame of discernment, and a basic probability assignment function is established. Then, as an intermediate result, a matrix of propositional transition probability is calculated. Finally, the future state can be obtained according to the current state. The proposed belief Markov model is a generalization of classical Markov chain and downward compatible with its properties. A case study shows that the limitations above mentioned are overcame and the proposed model is more effective and practicable.